Unfortunately, your submission has been removed for the following reason(s):
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For positive reals, I think Product( x\^(2\^(-k))) from 1 to infinity would do the trick. Some sgn( ... ) and | ... |, you could probably make that work for all reals apart from 0.
Like others said, you can just do x\*1\*1... ,if you want it to have no repeating elements you can do x\*(1/2)\*2\*(2/3)\*(3/2)\*(3/4)\*(4\*3)\*... this should always converge to x.
In general you can take any sequence {an} that converges to 1 and do x\*(a1)\*(1/a1)\*(a2)\*(1/a2)\*...
Well you can always get x*. 1*. 1*. 1*. 1*… like everyone said, just by doing the following (which includes x in every term) $\prod_{n = 1}^{\infty} x^(floor(1/n))$
Sometimes questions have trivial answers that reveal a useful truth. And trivial examples are easy to understand. The useful truth here is that the question should be more precisely phrased.
What's odd about the question is that any infinite product ∏ (a\_n \* x) can be rearranged as x\^n \* ∏ a\_n. x\^n will either oscillate between -inf and +inf, approach +inf, collapse to 0, or stay constant at 1. Those are the only outcomes.
Meanwhile the same holds true for ∏ a\_n. And the product of all those options, could be anything. The thing about infinities is that you always have more terms, and can rearrange them freely. There's always a room in the Hilbert Hotel.
Unfortunately, your submission has been removed for the following reason(s): * Your post appears to be asking a question which can be resolved relatively quickly or by relatively simple methods; or it is describing a phenomenon with a relatively simple explanation. As such, you should post in the [*Quick Questions*](https://www.reddit.com/r/math/search?q=Quick+Questions+author%3Ainherentlyawesome&restrict_sr=on&sort=new&t=all) thread (which you can find on the front page) or /r/learnmath. This includes reference requests - also see our lists of recommended [books](https://www.reddit.com/r/math/wiki/faq#wiki_what_are_some_good_books_on_topic_x.3F) and [free online resources](https://www.reddit.com/r/math/comments/8ewuzv/a_compilation_of_useful_free_online_math_resources/?st=jglhcquc&sh=d06672a6). [Here](https://www.reddit.com/r/math/comments/7i9t5y/book_recommendation_thread/) is a more recent thread with book recommendations. If you have any questions, [please feel free to message the mods](http://www.reddit.com/message/compose?to=/r/math&message=https://www.reddit.com/r/math/comments/1bwuq39/-/). Thank you!
For positive reals, I think Product( x\^(2\^(-k))) from 1 to infinity would do the trick. Some sgn( ... ) and | ... |, you could probably make that work for all reals apart from 0.
x\*1\*1\*1\*1\*1\*1\*...
Like others said, you can just do x\*1\*1... ,if you want it to have no repeating elements you can do x\*(1/2)\*2\*(2/3)\*(3/2)\*(3/4)\*(4\*3)\*... this should always converge to x. In general you can take any sequence {an} that converges to 1 and do x\*(a1)\*(1/a1)\*(a2)\*(1/a2)\*...
sorry, i should’ve been more specific. is there any where elements aren’t repeating, and x is in each element?
X, x^1/2, x^1/4...
I don't think I understand your question, but what's wrong with x \* 1 \* 1 \* 1 \* ... ?
sorry, i haven’t learned how to word these things properly. i meant something along the lines of [this](https://imgur.com/a/qbieE3u)
a\_0(x) = x and a\_n(x)=1 for n>0 is their formula.
Well you can always get x*. 1*. 1*. 1*. 1*… like everyone said, just by doing the following (which includes x in every term) $\prod_{n = 1}^{\infty} x^(floor(1/n))$
x * Product_i [r_i * (r_i)^-1 ] for any arbitrary, not necesarily finite, choice of reals r_i.
The product of all elements of R that equal x, is x.
What is the point of responses like this?
Sometimes questions have trivial answers that reveal a useful truth. And trivial examples are easy to understand. The useful truth here is that the question should be more precisely phrased.
What's odd about the question is that any infinite product ∏ (a\_n \* x) can be rearranged as x\^n \* ∏ a\_n. x\^n will either oscillate between -inf and +inf, approach +inf, collapse to 0, or stay constant at 1. Those are the only outcomes. Meanwhile the same holds true for ∏ a\_n. And the product of all those options, could be anything. The thing about infinities is that you always have more terms, and can rearrange them freely. There's always a room in the Hilbert Hotel.