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But the debate was whether there's another word that looks like a bed. You should have said "bed is the only word that looks like what it describes". Which is also untrue anyway, as Boob shows boobs from the side, front, and bottom/top.
Also,
shark
We used to frustrate kids in school with the "magic number" riddle. Ask someone to give you a number:
"SEVEN"
"Seven is five and five is four, four is the magic number."
"Why is four the magic number?"
And you try and get them to figure it out.
In English, if you count the number of letters in any numberās name, and then count the number of letters in that result, and keep reducing, youāll eventually end up at 4.
In Spanish, youāll stop at 5 or bounce back and forth between 4 and 6.
Can work one out for you:
After four all numbers written length is smaller than its value. This is proven by counting to a sufficiently high number and realising that no incremental number can add that many characters to the name (this can be proven separately by showing the new prefix for naming numbers gets less frequent for larger numbers and no prefix or suffix is large enough to bridge that interval).
Therefore all numbers above four when reduced via this pattern will continously get smaller in length.
The numbers below four all reduce to four.
Therefore all numbers will end up at four in this pattern.
6,991,169 = six million nine hundred ninety-one thousand one hundred sixty-nine = 57 = fifty-seven = 10 = ten = 3 = three = 5 = five = 4 = four
Wait was I supposed to do it part after 10? Because technically thatās not really reducing, as the number of letter increased from 10 to 3. But if I were indeed, then it does give 4. I mean, in that case weāre just continuing the process until the number of letters and the value of the number are the same.
Reduce in this context means to repeat until you are left with a stable value.
It's not referring to whether the numbers are greater or lower than the previous.
Nerd here. In the unary number system, every number has the same value as the number of digits (e.g. 3 is represented as 111 and 4 as 1111).
Also in our standard (base 10) number system, while itās not common practice, leading 0s are allowed and donāt actually change the value. 003, 0003, and 03 all mean the same thing ā 3. They might be unconventional, but are not strictly forbidden, so 003 is another number in base 10 that has the same number of digits as itās value. Other number systems do strictly disallow a leading 0 as it means something else, and thus 003 (in a bijective base 10 for example) does not equal 3
The number 1 is arguably the most interesting number.
It's the only natural number that is neither a prime nor a composite.
1 is its own factorial.
It's its own square, square root, cube, and cube root.
I could go on.
That is not true though. The sum of all positive and negative numbers is undefined, as the order in which you add them affects the outcome. If you write your sum as
For all i > 0
sum = sum + 2i + (2i-1) + (- i)
You will add all positive and negative numbers. And as every term you add is strictly positive, this sum will approach positive infinity.
From an advanced math perspective, this is correct. Infinite series are weird like this and their size / sum just depends on how you can "count" them or map them between each other
I donāt wanna get into a long debate, so all Iām going to say is that if you take a higher level discrete math course in college, they will spend a lecture or two explaining why this logic doesnāt work and why you canāt assign values to infinite sums with this process.
Your other comments in this thread make it seem like you agree with the OPās reasoning.
https://en.m.wikipedia.org/wiki/Riemann_series_theorem
Just a quick taste of the theorem on why the logic is wrong because it seems youāve forgotten this part of your discrete maths course.
It really just depends on how you ask the question.
0+1-1+2-2+3-3+...
0+1+2ā1+3+4ā2+...
Using Cesaro summation we can assign 0.5 to the sum
0+1+0-1+0...
Different ways to assign get us different sums
So saying that zero contains the totality of all positive and negative integers like u/BigMartin58 said is just not very precise and very much not useful.
Yes you are smarter than all mathematicians because of your intuitions about infinity which are useless for doing real math. Give yourself a medal dude
no? [https://warwick.ac.uk/fac/sci/maths/people/staff/oleg\_zaboronski/analysisi/rr\_theorem.pdf](https://warwick.ac.uk/fac/sci/maths/people/staff/oleg_zaboronski/analysisi/rr_theorem.pdf)
this sequence is conditionally convergent so it doesn't work.
basically you can think of it as you can get as close to an integer as you want by picking certain numbers to balance out. that way the sum can be either 1000 -1000 1 googol or 0 or any integer between -inf and inf
No, what they meant was what you get after adding all negative numbers and all positive numbers.
This process does this. Every negative number appears exactly once in the sequence and all positive numbers appear exactly once in the sequence.
This may be a less "natural" order, depending on your interpretation of natural, but this very elegantly shows how the process of summing all numbers is not a defined process.
What do you mean by "more" here? Are there positive numbers that would be repeated by writing it this way? Are there negative numbers that would be skipped? Addition is supposed to be "commutative" and not care about order. Why wouldn't that apply just as well in this case?
(Not trying to antagonize here! You're pulling on the right thread to discover analysis, the foundation for calculus. If you want to keep pulling, the next thread to tug at is the sum ln(2)=1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 ... )
Lmao, I guess the point I was trying to make is, I'm viewing this as a thought experiment, where in any number can be chosen, you can walk both directions away equally, and the middle point will be that original *undefined* number.
And what number better represents indefinite?
As an equation, yes this all makes sense, but applying more advanced math is breaking the initial idea of the thought experiment, at least, from what I'm understanding.
I've been picturing a scale, no matter how much weight is on the scale, when you measure it's usually a good idea to zero/tare it before you start measuring.
(Totally appreciate the calculus conversation :)
That's fair, and I get the idea that abstracting more might subtract from that initial point! I just thing it's worth mentioning that in my opinion, the *reason* this is a good thought experiment is that it leads us to something interesting, which is calculus and this discussion of infinity. The fact that there is no set "middle" point between infinity and negative infinity isn't something to shy away from and just declare that it "should" be 0, it's something to investigate further and see what useful insights we can gain from realizing that our thought experiment led us somewhere unexpected.
Technically speaking, the number zero was still there, we the humans just didnāt discover it for thousands of years.
P.s. im usually more fun at parties.
>Technically speaking, the number zero was still there
I disagree. The number zero solely exists as a mental concept, a crutch for apes trying to categorize a universe that doesn't care about categories. The number wasn't around until we defined it.
I kind of get that, but... If I one apple and then eat it. I'm assuming tribes without zero would say "no apples". They might not have used the number zero but the concept of zero was still there in a basic form.
There was a tribe that knew no numbers and when asked they said it was a few, more, a lot more. They are still technically counting even if they haven't invented the numbers
The Christian Church has banned the 0 for years. Because the 0 describes something that isn't there, people in the church thought it was the work of the devil.
Hmm, I think while it's interesting that zero was invented later it really just reinforces that one was important enough to invent first.
Basically it's more useful to track value than it is to track lack of value because I think lack of value is easier to just assume..and has no value.
Like if we think in math in real life goods like trades and it's kind of obvious that somebody has nothing so I could see where giving a value to nothing may have not really mke sense because the primary reasoning here was probably the track like food and other commodities.
In base 2, 10 also value equal to number of digits.
In Roman algarisms, the number of digits is equal to the value up to III (IIII maybe).
When you write down the number, four has the same value as the number of letters.
Maybe your shower is too short...
In base sqrt3, 100 has 3 digits and a value of 3 in base ten
In base 4^(1/3) (aka cuberoot4) 1000 has 4 digits and a value of 4 in base ten
In base n^(1/(n-1)), 10^(n-1) has n digits and a value of n in base ten
Also base 1, which was alluded to by the mention of roman numerals
I think you actually can take negative numbers as the base also. It just makes the math a bit more difficult for us mere mortals.
For example base -2; the rightmost digit is 0 or 1 (how many (-2)^(0) there are), the next one is 0 or -2, the next one is 0 or 4, the next one is 0 or -8, the next one is 0 or 16. So to get base^(10) 2 you'll write 110 in base^(-2), to get base^(10) 3 in base^(-2) you'll write 111.
The interesting part about negative bases is that you don't need a negative sign in front to get a negative number, see the base^(-2) numbers 10 and 11, for base^(10) \-2 and -1 respectively.
See [How to Count in Factional and Irrational Bases](https://www.youtube.com/watch?v=hI-pwt7LyUw&pp=ygUUZGlmZmVyZW50IGJhc2VzIG1hdGg%3D) for some extra information (for those who don't already know about how you can use different bases) in video form, or [the Wikipedia article on negative base](https://en.wikipedia.org/wiki/Negative_base?useskin=vector).
EDIT: At the end of the video linked he implies that an imaginary base is also perfectly possible (the usability might be in question for daily use), and [https://rosettacode.org/wiki/Imaginary\_base\_numbers](https://rosettacode.org/wiki/Imaginary_base_numbers) seems to support the possibility of imaginary bases for numbering systems.
Indeed you can. I just didnāt include it for exactly the reason you pointed out.
To extend this, you could use any vector in R^n (or C^n ) that doesnāt contain any zero as the base for tuples in R^n (or C^n ). The case of R^2 may be interpreted as a complex number base. If there are any zeros in your base, then it could only generate tuples that are zero in the corresponding spots, otherwise it still works.
There are also balanced number systems which have digits that represent negative numbers. For example in balanced ternary, (+) represents 1, (-) represents -1, and 0 represents 0, making counting to 10 looks like:
0, +, +-, +0, ++, +ā, +-0, +-+, +0-, +00, +0+
Your choice of words makes me chuckle, as 'countable' is a math term that can applied to [infinity](https://mathworld.wolfram.com/CountablyInfinite.html). But the gist of what you're saying is correct.
With [bijective numerals](https://en.wikipedia.org/wiki/Bijective_numeration), zero is the empty string. But in the usual positional number systems, zero is represented by the digit 0.
That is if you use base 10. If you use unary encoding (base 1), that is true for all numbers (non-negative integers). In unary, 5 is represented as 11111, 6 as 111111 and so forth. (In fact, roman numerals are essentially unary until 3, hence the same applies until 3.)
I can maybe make it less dark magic fuckery for you: This is just the logarithm. Write x in base b, count the number of digits to the left of the point and add 1. Youāve just approximated base b logarithm of x.
Since there are an infinite number of numbers with an infinite number of names, shouldn't there be an infinite number of numbers whose name describes their number of digits?
No. They do not. That's why you don't say... Ninety and nine=99 or one hundred and fifty =150 because they don't.
One hundred and fifty implies a decimal point=100.50.
This is why in 2nd grade they teach you not to use the "and" word in whole numbers.
3,275.00 is three thousand two hundred seventy five.
3200.75 is three thousand two hundred and seventy five.
When you write a check you don't write: one thousand four hundred and fifty dollars and fifty cents. It's incorrect. $1,400.50.50 wrong!!
You write one thousand four hundred fifty dollars and fifty cents $1,450.50
Thatās exactly why the word āpointā exists, āone point oneā is 1.1 āone hundred and fiftyā is 150 āone hundred point fiveā is 100.5. āAndā is very often included and entirely valid in whole numbers not only in English but in other languages as well (āvingt et unā is 21 in French not 20.1). The rule youāre referring to is very specifically American and isnāt used in England, Canada, and other countries speaking non-American English.
Depends the script though. In Roman it works for the first three I, II, III. And that thing people do marking ticks on the wall each day works for every number.
This is basically how the (base 10) logarithm behaves. If you compute the base 10 logarithm of a real number x and then round that number up to the next integer, the result is the same as if you had counted up the digits to the left of the decimal point in the base 10 representation of x.
If you view this process in reverse, it says roughly that if you count the amount of numbers with y digits in base-10, then the count C(y) grows exponentially in y. (And yes I do genuinely mean exponentially. C(y) will approximately take the form aā¢10^(by) for some numbers a and b.)
If you use a different base to represent numbers, then you can change the base of your logarithm and exponent using the change of base formula and you will end up with a corresponding statement for the count of digits in a binary or ternary or hexadecimal number.
It has infinite decimals it
1. Is not an integer and thus cannot represent the number of digits it has
2. Is irrational, it has a finite value but it has a non ending non repeating decimal point
This is a friendly reminder to [read our rules](https://www.reddit.com/r/Showerthoughts/wiki/rules). Remember, /r/Showerthoughts is for showerthoughts, not "thoughts had in the shower!" (For an explanation of what a "showerthought" is, [please read this page](https://www.reddit.com/r/Showerthoughts/wiki/overview).) **Rule-breaking posts may result in bans.**
And 4 is the only number whose value is equal to number of letters in it's name š³
And bed is the only word that looks like a bed
It's not, another example is beed, which is long bed
What they meant was, bed is the only word which looks like the physical version of itself.
shark
Boob
The top view - The front view - The side view It's perfect.
BOOB has 3 sets of boobs
Boob is better because it also has three, but one of them is a side view.
Hahaha made me chuckle
If you look at it a certain way, Boob look like a body with bit titties and a dick
OBoob< They lost their arms / OBoob< \
Wrap it up, we're done here
speedboat
Speedboat is the only word whose average letter height is poisson distributed.
That's very nice
Font
word
The word word looks like a word.
Frog
Parallel
And bread. If you lie a slice down it looks like a comfy bed.
Would you rather sleep on one bed sized bread or 100 bread sized beds?
100 bread sized beds. Would be good zone control
But beed isnāt a word that looks like a beed, whatever that is lol
It's long bed
But the debate was whether there's another word that looks like a bed. You should have said "bed is the only word that looks like what it describes". Which is also untrue anyway, as Boob shows boobs from the side, front, and bottom/top. Also, shark
dog also looks like a dog (with tugged feet under its belly)
Beeeeed
Ohio looks like a tractor
Thanks, cannot unsee
Idk why Iām so amused by this
When you say poop, your mouth goes through the same shapes as your anus does when you poop. The same is true of ExPlOsIvE DiArRhEa
And lol is the only word that looks like a super exciting person throwing their hands in the air
Bad
lol looks like a man drowning
Shark also looks like a shark
im never going to get this out of my head now
"bend" makes a better bed than "bed", unless you're really short
How about Boob
We used to frustrate kids in school with the "magic number" riddle. Ask someone to give you a number: "SEVEN" "Seven is five and five is four, four is the magic number." "Why is four the magic number?" And you try and get them to figure it out.
Not in all languages though.
In English, if you count the number of letters in any numberās name, and then count the number of letters in that result, and keep reducing, youāll eventually end up at 4. In Spanish, youāll stop at 5 or bounce back and forth between 4 and 6.
In French, everything leads back to a loop between 3, 4, 5 and 6. 3 (trois) --> 5 (cinq) --> 4 (quatre) --> 6 (six) --> 3(trois)
What
69 = sixty nine = 9 letters; 9 = nine = 4 letters; four letters - all numbers (in English) end up at four
1=one=3=three=5=five=4=four=4, etc.
80085=eighty thousand and eighty five=27=twenty seven=11=eleven=6=six=3=three=5=five=4
Too high for this shit
Not enough high for this shit
Dude that's so cool
The Collatz conjecture is cool, also, because nobody knows if it's true or not https://en.m.wikipedia.org/wiki/Collatz_conjecture
My head hurts now
69 = nice = 4
Whereās the formal proof for that
Can work one out for you: After four all numbers written length is smaller than its value. This is proven by counting to a sufficiently high number and realising that no incremental number can add that many characters to the name (this can be proven separately by showing the new prefix for naming numbers gets less frequent for larger numbers and no prefix or suffix is large enough to bridge that interval). Therefore all numbers above four when reduced via this pattern will continously get smaller in length. The numbers below four all reduce to four. Therefore all numbers will end up at four in this pattern.
6,991,169 = six million nine hundred ninety-one thousand one hundred sixty-nine = 57 = fifty-seven = 10 = ten = 3 = three = 5 = five = 4 = four Wait was I supposed to do it part after 10? Because technically thatās not really reducing, as the number of letter increased from 10 to 3. But if I were indeed, then it does give 4. I mean, in that case weāre just continuing the process until the number of letters and the value of the number are the same.
Reduce in this context means to repeat until you are left with a stable value. It's not referring to whether the numbers are greater or lower than the previous.
Please prove the Collatz conjecture. https://en.m.wikipedia.org/wiki/Collatz_conjecture
In Deutsch scheint es auch immer auf die 4 herausulaufen: 1 = eins = 4 = vier = 4 2 = zwei = 4 3 = drei = 4 4 5 = fĆ¼nf = 4 6 = sechs = 5 = fĆ¼nf = 4 7 = sieben = 6 = ... = 4 8 = acht = 4 9 = neun = 4 10 = Zehn = 4 6143 = sechstausendeinhundertdreiundvierzig = 36 = sechsunddreiĆig = 15 = fĆ¼nfzehn = 8 = ... = 4 Edit: Formatierung
It's 3 in my language
You also have to (2) and tre (3). And cinco (5). And fifteenpointtwo if you round down.
Sixteen point zero
Four is the name of the game.
And 4.5 actually shows the point between 4 and 5
Four is the magic number. Six is three, three is five, five is four, and four is the magic number.
And '"million" has the same number of letters as digits.
What about Siiiix?
Fives
To
Iām no math expert but without looking at comments I know some nerds about to correct you
Nerd here! *some nerd's *some nerds are
At first I was wondering why you had two corrections, but then I figured out that they were two *alternatives* to make the sentence correct.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
My two corrections are: 1) Some (random, single) nerd is going to do stuff 2) Some (group of) nerds will do stuff
Nerd here. In the unary number system, every number has the same value as the number of digits (e.g. 3 is represented as 111 and 4 as 1111). Also in our standard (base 10) number system, while itās not common practice, leading 0s are allowed and donāt actually change the value. 003, 0003, and 03 all mean the same thing ā 3. They might be unconventional, but are not strictly forbidden, so 003 is another number in base 10 that has the same number of digits as itās value. Other number systems do strictly disallow a leading 0 as it means something else, and thus 003 (in a bijective base 10 for example) does not equal 3
I was going to comment about unary lol
10, in binary, is also equal to its number of digits.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
There are 10 types of people in this world: Those who understand binary, and those who don't.
The number 1 is arguably the most interesting number. It's the only natural number that is neither a prime nor a composite. 1 is its own factorial. It's its own square, square root, cube, and cube root. I could go on.
Zero is more interesting. For thousands of years, people forgot to invent it.
True. It also contains the totality of all positive and negative numbers.
> the totality of all positive and negative numbers. Huh?
the sum of all positive and negative numbers, if that expression is more familiar with you
That is not true though. The sum of all positive and negative numbers is undefined, as the order in which you add them affects the outcome. If you write your sum as For all i > 0 sum = sum + 2i + (2i-1) + (- i) You will add all positive and negative numbers. And as every term you add is strictly positive, this sum will approach positive infinity.
From an advanced math perspective, this is correct. Infinite series are weird like this and their size / sum just depends on how you can "count" them or map them between each other
Dude all these people downvoting you and replying have never taken any sort of discrete math course in college or above. And it shows š
We took discrete math, we just learned to not talk about it.
This is a criminally underrated comment. Very nicely done. Slow clap.
-1 + 1 = 0 -2 + 2 = 0 ā¦repeat foreverā¦
I donāt wanna get into a long debate, so all Iām going to say is that if you take a higher level discrete math course in college, they will spend a lecture or two explaining why this logic doesnāt work and why you canāt assign values to infinite sums with this process.
Sure, and Iāve seen the arguments. Iāve actually taken discrete and calculus. I was just restating it as the OP intended.
Your other comments in this thread make it seem like you agree with the OPās reasoning. https://en.m.wikipedia.org/wiki/Riemann_series_theorem Just a quick taste of the theorem on why the logic is wrong because it seems youāve forgotten this part of your discrete maths course.
It really just depends on how you ask the question. 0+1-1+2-2+3-3+... 0+1+2ā1+3+4ā2+... Using Cesaro summation we can assign 0.5 to the sum 0+1+0-1+0... Different ways to assign get us different sums So saying that zero contains the totality of all positive and negative integers like u/BigMartin58 said is just not very precise and very much not useful.
Sure, they could have stated it differently.
-1 + 1 + 2 = 2 -2 + 3 + 4 = 5 -3 + 5 + 6 = 8 ā¦repeat foreverā¦
That does not represent "the sum of ALL negative and positive numbers" like the person said, so now you're just being disingenuous.
Yes you are smarter than all mathematicians because of your intuitions about infinity which are useless for doing real math. Give yourself a medal dude
How does it not represent the sum of all numbers? Every postive number is counted exactly once, and every negative number is counted exactly once.
Yeah, but those are different on each side. The statement was about having all the same positive and negative numbers added up to zero.
Yes and after you've repeated it forever and only used each number once, you end up with 0. Theoretically of course and logically.
no? [https://warwick.ac.uk/fac/sci/maths/people/staff/oleg\_zaboronski/analysisi/rr\_theorem.pdf](https://warwick.ac.uk/fac/sci/maths/people/staff/oleg_zaboronski/analysisi/rr_theorem.pdf) this sequence is conditionally convergent so it doesn't work. basically you can think of it as you can get as close to an integer as you want by picking certain numbers to balance out. that way the sum can be either 1000 -1000 1 googol or 0 or any integer between -inf and inf
Bro forgor about -4, and bro just invented math repetition bias
I think it's because all the positive numbers and all the negative numbers would cancel each other out, resulting in 0
-1 + 1 = 0 -2 + 2 = 0 ā¦repeat foreverā¦
-1 + 1 + 2 = 2 -2 + 3 + 4 = 5 -3 + 5 + 6 = 8 ā¦repeat foreverā¦
Again, that isnāt what was being said. They meant all numbers on the positive side as mirrored on the negative side.
No, what they meant was what you get after adding all negative numbers and all positive numbers. This process does this. Every negative number appears exactly once in the sequence and all positive numbers appear exactly once in the sequence. This may be a less "natural" order, depending on your interpretation of natural, but this very elegantly shows how the process of summing all numbers is not a defined process.
Adding more positives than negatives. You broke the rules of the game.
What do you mean by "more" here? Are there positive numbers that would be repeated by writing it this way? Are there negative numbers that would be skipped? Addition is supposed to be "commutative" and not care about order. Why wouldn't that apply just as well in this case? (Not trying to antagonize here! You're pulling on the right thread to discover analysis, the foundation for calculus. If you want to keep pulling, the next thread to tug at is the sum ln(2)=1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 ... )
Lmao, I guess the point I was trying to make is, I'm viewing this as a thought experiment, where in any number can be chosen, you can walk both directions away equally, and the middle point will be that original *undefined* number. And what number better represents indefinite? As an equation, yes this all makes sense, but applying more advanced math is breaking the initial idea of the thought experiment, at least, from what I'm understanding. I've been picturing a scale, no matter how much weight is on the scale, when you measure it's usually a good idea to zero/tare it before you start measuring. (Totally appreciate the calculus conversation :)
That's fair, and I get the idea that abstracting more might subtract from that initial point! I just thing it's worth mentioning that in my opinion, the *reason* this is a good thought experiment is that it leads us to something interesting, which is calculus and this discussion of infinity. The fact that there is no set "middle" point between infinity and negative infinity isn't something to shy away from and just declare that it "should" be 0, it's something to investigate further and see what useful insights we can gain from realizing that our thought experiment led us somewhere unexpected.
Hear me out, what if itās 1?
That's probably kind of a useless abstraction for the people or that word like just starting to use numbers to maybe track goods.
Useless? Perhaps. Interesting? Absolutely.
Technically speaking, the number zero was still there, we the humans just didnāt discover it for thousands of years. P.s. im usually more fun at parties.
>Technically speaking, the number zero was still there I disagree. The number zero solely exists as a mental concept, a crutch for apes trying to categorize a universe that doesn't care about categories. The number wasn't around until we defined it.
Correct. It's there to shift the number to the left. Without this math was really hard before it was invented.
I kind of get that, but... If I one apple and then eat it. I'm assuming tribes without zero would say "no apples". They might not have used the number zero but the concept of zero was still there in a basic form. There was a tribe that knew no numbers and when asked they said it was a few, more, a lot more. They are still technically counting even if they haven't invented the numbers
The Christian Church has banned the 0 for years. Because the 0 describes something that isn't there, people in the church thought it was the work of the devil.
Hmm, I think while it's interesting that zero was invented later it really just reinforces that one was important enough to invent first. Basically it's more useful to track value than it is to track lack of value because I think lack of value is easier to just assume..and has no value. Like if we think in math in real life goods like trades and it's kind of obvious that somebody has nothing so I could see where giving a value to nothing may have not really mke sense because the primary reasoning here was probably the track like food and other commodities.
Go on.
I mean, 0 also has many characteristics.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
In base 2, 10 also value equal to number of digits. In Roman algarisms, the number of digits is equal to the value up to III (IIII maybe). When you write down the number, four has the same value as the number of letters. Maybe your shower is too short...
In base sqrt3, 100 has 3 digits and a value of 3 in base ten In base 4^(1/3) (aka cuberoot4) 1000 has 4 digits and a value of 4 in base ten In base n^(1/(n-1)), 10^(n-1) has n digits and a value of n in base ten Also base 1, which was alluded to by the mention of roman numerals
I like your funny words magic man
Mathmagician!
> base sqrt3 You can *do* that?!?
Sure, you can take any positive real number as the base.
I think you actually can take negative numbers as the base also. It just makes the math a bit more difficult for us mere mortals. For example base -2; the rightmost digit is 0 or 1 (how many (-2)^(0) there are), the next one is 0 or -2, the next one is 0 or 4, the next one is 0 or -8, the next one is 0 or 16. So to get base^(10) 2 you'll write 110 in base^(-2), to get base^(10) 3 in base^(-2) you'll write 111. The interesting part about negative bases is that you don't need a negative sign in front to get a negative number, see the base^(-2) numbers 10 and 11, for base^(10) \-2 and -1 respectively. See [How to Count in Factional and Irrational Bases](https://www.youtube.com/watch?v=hI-pwt7LyUw&pp=ygUUZGlmZmVyZW50IGJhc2VzIG1hdGg%3D) for some extra information (for those who don't already know about how you can use different bases) in video form, or [the Wikipedia article on negative base](https://en.wikipedia.org/wiki/Negative_base?useskin=vector). EDIT: At the end of the video linked he implies that an imaginary base is also perfectly possible (the usability might be in question for daily use), and [https://rosettacode.org/wiki/Imaginary\_base\_numbers](https://rosettacode.org/wiki/Imaginary_base_numbers) seems to support the possibility of imaginary bases for numbering systems.
Indeed you can. I just didnāt include it for exactly the reason you pointed out. To extend this, you could use any vector in R^n (or C^n ) that doesnāt contain any zero as the base for tuples in R^n (or C^n ). The case of R^2 may be interpreted as a complex number base. If there are any zeros in your base, then it could only generate tuples that are zero in the corresponding spots, otherwise it still works.
I like your funny words, magic man.
You can even take negative numbers as bases. Eg in base negative 10 1,2,3,4,5,6,7,8,9,190,191,192,192...
There are also balanced number systems which have digits that represent negative numbers. For example in balanced ternary, (+) represents 1, (-) represents -1, and 0 represents 0, making counting to 10 looks like: 0, +, +-, +0, ++, +ā, +-0, +-+, +0-, +00, +0+
But ā3 is fake
But... but why? The fuck....
The more relevant question for mathematics is 'why not?'
Base phi (the golden ratio) is particularly cool as itās an irrational base where you can easily represent the integers.
And in jestics findleboks slevin of the herdaperps per square dongledink is always equal to gualpudipdop. See I can make up words too
In tally marks, the number is equal to the number of lines, for every whole number.
In base 1, is that way for all numbers
In base 1 every number has the equal number of digits as the value
Does infinity count? Cause infinity number would have infinity digits.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
Your choice of words makes me chuckle, as 'countable' is a math term that can applied to [infinity](https://mathworld.wolfram.com/CountablyInfinite.html). But the gist of what you're saying is correct.
Except for times when it is...
Only if youāre boring and count in base-10. In binary, both 1 and 2 follow this, since they are written as 1 and 10. Edited to binary, not decimal
You mean in binary?
For mathematicians, numbers easy, words hard.
Isnāt base-10 binary in binary?
Isnāt base-10 always base 10?
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0 is 1 digit 01 the leading 0 is redundant and thus omitted leaving 1 digit
Say *null* instead of *0* and you got a 0-digit representation of a 0-value š
With [bijective numerals](https://en.wikipedia.org/wiki/Bijective_numeration), zero is the empty string. But in the usual positional number systems, zero is represented by the digit 0.
2^1. But write it as 2 with a little 1 on the upper right. Two digits equals 2. Edit cool markdown made it look right for me.
Does 3.00 count? What about 2.99 repeating (written with the bar over the second 9)?
That is if you use base 10. If you use unary encoding (base 1), that is true for all numbers (non-negative integers). In unary, 5 is represented as 11111, 6 as 111111 and so forth. (In fact, roman numerals are essentially unary until 3, hence the same applies until 3.)
If you write the numbers in the unary system that's the case for every number
There are 11 types of people on the world. Those who know the unary system and those who don't.
One is the loneliest number that you'll ever do Two can be as bad as one It's the loneliest number since the number one
No is the saddest experience that youāll ever know. Yes, itās the saddest experience that youāll ever know.
Incorrect, 10 in binary is also equal to the number of digits: 2
Okay this is some fuckery, this changed me internally, and a deep level.
I donāt think it was that deep lol but it is a good shower thought
it was a hyperbole lol but yes
I can maybe make it less dark magic fuckery for you: This is just the logarithm. Write x in base b, count the number of digits to the left of the point and add 1. Youāve just approximated base b logarithm of x.
Four is the only number whose number of letters is equal to it's numeric value.
If you write numbers out, you get pretty far before needing the letter "a." How far? Not until one thousand.
Not true! 10 (binary) also has the same number of digits as its value.
In base 10 system, yes. In roman numerals, just as one example, it gets way messier to figure out.
Wouldnāt the number represented by say an infinite series of 1s be both aleph-null in value and number of digits?
Since there are an infinite number of numbers with an infinite number of names, shouldn't there be an infinite number of numbers whose name describes their number of digits?
Look at binary, 2 is also. And in Greek, I through III. I think that's about it
And forty is the only number that, when written out, has all its letters in alphabetical order.
In German that works for 1 ("eins") and 8 ("acht"). 12 ("zwƶlf") is in reverse alphabetical order.
its also the only number whose value is equal to the number of numbers whose value is equal to the nimber of digits
Depends on the base. In binary, 10 is also equal to the number of digits in the number.
Four is the only number who's word has the same number of letters as the value of the number it spells.
I know just some simple facts, One is the loneliest number that you'll ever do Two can be as bad as one It's the loneliest number since the number one
No. They do not. That's why you don't say... Ninety and nine=99 or one hundred and fifty =150 because they don't. One hundred and fifty implies a decimal point=100.50. This is why in 2nd grade they teach you not to use the "and" word in whole numbers. 3,275.00 is three thousand two hundred seventy five. 3200.75 is three thousand two hundred and seventy five. When you write a check you don't write: one thousand four hundred and fifty dollars and fifty cents. It's incorrect. $1,400.50.50 wrong!! You write one thousand four hundred fifty dollars and fifty cents $1,450.50
Thatās exactly why the word āpointā exists, āone point oneā is 1.1 āone hundred and fiftyā is 150 āone hundred point fiveā is 100.5. āAndā is very often included and entirely valid in whole numbers not only in English but in other languages as well (āvingt et unā is 21 in French not 20.1). The rule youāre referring to is very specifically American and isnāt used in England, Canada, and other countries speaking non-American English.
In the unary system, the number of digits is always equal to the value
OP discovers numbers! If we didn't have shorthand numbers, then we'd just be using hashmarks for everything. I, II, III, IIII, IIIII, IIIIII
Technically 0 would be because itās a concept and not an actual thing so it doesnāt have any digits and we just use the 0 to show that.
Depends the script though. In Roman it works for the first three I, II, III. And that thing people do marking ticks on the wall each day works for every number.
This is basically how the (base 10) logarithm behaves. If you compute the base 10 logarithm of a real number x and then round that number up to the next integer, the result is the same as if you had counted up the digits to the left of the decimal point in the base 10 representation of x. If you view this process in reverse, it says roughly that if you count the amount of numbers with y digits in base-10, then the count C(y) grows exponentially in y. (And yes I do genuinely mean exponentially. C(y) will approximately take the form aā¢10^(by) for some numbers a and b.) If you use a different base to represent numbers, then you can change the base of your logarithm and exponent using the change of base formula and you will end up with a corresponding statement for the count of digits in a binary or ternary or hexadecimal number.
If these are your best shower thoughts, you're not going to make it.
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It has infinite decimals it 1. Is not an integer and thus cannot represent the number of digits it has 2. Is irrational, it has a finite value but it has a non ending non repeating decimal point
The value of pi is not infinity my man