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September 5th, 2017, 07:12 PM   #1
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Infinity proof?

Another proof in the making. There may be some mistakes in this one, feel free to let me know what to do to ensure it's correct.
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September 5th, 2017, 07:16 PM   #2
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This proof seems to show no errors or miscalculations - well done. As correct as it is, by intuition, I cannot bring myself to agree with it.
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September 5th, 2017, 07:19 PM   #3
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Seems to be correct. However, a flaw like that would have surely been picked up by now and would not be accepted as correct. Great job though!
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September 5th, 2017, 07:19 PM   #4
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Is this a really necessary proof? While it is correct, what is the purpose?
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September 5th, 2017, 07:23 PM   #5
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I agree to some degree, but this kind of stems from doing it for no reason. To me it doesn't need a reason other than to just express a mathematical idea. Thanks for the reply though
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September 5th, 2017, 07:23 PM   #6
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Your expression $S_\infty$ is finite (everywhere that it is valid). So you've proved nothing about multiplying $\infty$.

Note that $\infty$ isn't a number anyway. Multiplication isn't defined for it.
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Last edited by v8archie; September 5th, 2017 at 07:29 PM.
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September 5th, 2017, 07:25 PM   #7
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Originally Posted by QEDboi View Post
I agree to some degree, but this kind of stems from doing it for no reason. To me it doesn't need a reason other than to just express a mathematical idea. Thanks for the reply though
you are a very admirable user of this forum, and it just shows your love for maths! While I still don't think there is a reason for this proof, you have impressed me
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September 5th, 2017, 07:25 PM   #8
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Hey, thanks for the feedback. Is there any way of doing a proof like this expressed in mathematical terms, or is the concept of infinity something more philosophical rather than mathematical?
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September 5th, 2017, 07:44 PM   #9
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There are various infinities defined in maths, but the $\infty$ you are talking about isn't one of them. That's just a notational shorthand. Some of the ones that are defined do have the property you state, others don't. But either way, you can't prove anything about any infinity using only finite numbers.
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September 5th, 2017, 07:46 PM   #10
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I did not read your proof except for the last line. It says: "Infinite is a closed set that can be multiplied upon."

As that makes no sense in terms of usual mathematical terminology, I assume the rest is based on misunderstandings and errors. No other conclusion is possible. Three concerns:

* For one thing you use "infinite" as a noun. Infinity is a noun, infinite is an adjective. I don't know if that's a conceptual error or a language issue.

* A closed set has a particular meaning in math, and it does not make any kind of sense at all to say that "infinity is a closed set." You might say something like, $[0, \omega]$ is a closed set in the order topology on the countable ordinals. That would be a true mathematical statement. Other than that I can't interpret your statement.

* And a "set that can be multiplied upon," I confess that I can't interpret at all.

Perhaps you can summarize your idea or terminology here in a more standard way. And just speaking personally, I prefer images to be right side up, block printed if your handwriting isn't perfectly readable, and well-lit and sharply focussed. But that's just me.

ps -- Your first line is wrong. You said: $\infty \ne n \infty, n \in \mathbb R$ (if I'm reading your handwriting correctly).

Now this is not only not true, it's "not even false." Since you haven't defined the symbol $\infty$, nor defined what you mean by multiplying a real number times $\infty$, you can't say the inequality is true or false. It's meaningless until you define your symbols.

It is certainly the case that if $n \in \mathbb N$ and $\kappa$ is any cardinal number, then $n \kappa = \kappa$. That's a basic fact about cardinal multiplication.

So in fact we can "multiply infinity," but only after we have made some precise definitions. But multiplying infinity by any finite number doesn't change the infinity, if by infinity you mean some transfinite cardinal.

I hope you will not be too dismayed by my criticism, but rather will be motivated to learn about the mathematics of infinity as it is currently understood. Your interests are certainly in the right place.

https://en.wikipedia.org/wiki/Cardinal_number

Last edited by Maschke; September 5th, 2017 at 08:27 PM.
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