Why I Don’t Like Something Approaching Infinity

Why I Don’t Like Something Approaching Infinity

In this discussion, I want to show you why I don’t like the idea of something approaching infinity, and I will also prove how the concept must be wrong. Through a simple analysis of mathematics, I will show that something of a finite value cannot ever equal something of infinity. First, what does it mean when a system is found to (have a property of infinity) as it approaches infinity?

This question comes from the ideas exchanged between me and DH, discussing exactly the nature of the universe and its expansion. DH said even though there may be no limit to expansion, it is not expanding infinitely yet, but will approach infinity. I argued this to be nonsense, because how can one define the expansion now, and a further expansion later, if there is no recourse in its directionality? In other words, if the universe expands forever, then surely its expansion is infinite now, rather than saying later it will reach infinity?

First of all, let’s go over some stuff related to these topics. We certainly define in math something approaching infinity, as this next equation shows, we can certainly express a finite number approaching infinity…

\(\lim_{x \to \infty}\frac{1}{x}=0\)

This is where the first logical inconsistency for me arises. If infinity is not defined, and if some finite and logical set of numbers approaches it, then where does the ill-defined nature of infinity come in? For a set of numbers to approach an undefined [number], the numbers before it must be very irrational. So the question would arise, where does infinity really start? If there is no set count to infinity, then one could very well say infinity started at any point.

Certainly, it has been shown that there is never always one infinity the same length of another infinity (Cantors Proof). So one infinity can be larger than another, and there appearance, it seems, does not have a rule at all. To bring about the second inconsistency, is a kind of logical argument. My mentor would call the following, an absurdity of logic.

You can say with a simple argument that you could have a number 1, 2 up to 207, all being finite numbers. To show how finite they really are, you can also state a final progression, \(\Omega\) and that no number can be larger than it. This symbol used, is of course, the Greek letter Omega, and we use it denote a boundary. But if one was to say, \(\Omega +1\), then this proposes a contradiction. It states that somehow there is one more than Omega, and that is a contradiction of terms because there can be no larger number than Omega.

In the same sense, if you have a finite number that approaches infinity, then a sense of absurdity arises, because how can one define the logical counting blocks up to some point which continues the same logic… for instance, if one counts from 1, 2, again up to 207, and finds infinity straight afterwards \(\lim_{x \to \infty}\), then what difference is it when saying \(\lim_{-\infty \to \infty}\) ? [1] If 1 is the boundary of some finite point, then arguable, even though the example above moving from 1 to 207 then to infinity, which is simple 208, 209, 210 and so on and so on, still has a finite limit of 1, so there is absolutely nothing unique that can distinguish \(\lim_{x \to \infty}\) and \(\lim_{-\infty \to \infty}\).

Now, back to the original question, how can a universe distinguish having an infinite expansion now, and one later as it may approach infinity, this can be shown in a more conservative manner. If 1 approaches infinity, then 1 can also equal infinity. This cannot be denied. In much the same sense, the ‘’supposed’’ finite expansion now of the universe very much equals the infinite expansion it approaches, if one assumes there is no recourse in its expansion, which evidence shows, there will not be. A simple mathematical illustration can show how absurd this is.

\(\infty = [\infty – (-\infty)]\)

\(\infty=2\infty\)

Now, if one combines the infinities,

\(1=2\frac{\infty}{\infty}\)

Which is where my example now shows the absurdity in the logic in trying to distinguish between a finite system and an infinite system entangled together. In the final equation, \(1=2\frac{\infty}{\infty}\), there is fallacy, because one assumes that infinity equals a finite number. Not only that, but if one takes my thoughts seriously in trying to distinguish the finite nature from the infinite nature in, [1], also shown below, then the finite having no distinction from having a nature easily expressed as being infinite, the fallacy above yields another fallacy, because one infinity over another is also undefined.

My final thoughts on this, concludes that it is very hard at best to imagine if not accept that (in the original example given), how one can say the universe is not in an infinite expansion now, as compared to some point it approaches. Infinity isn’t even a destination!! This is the truth I speak, infinity is not a destination, but rather a directionality, according to modern mathematics.

If infinity isn’t even a destination, what is it we are implying when something approaches infinity, and what does it imply when the universe approaches it? In the end, isn’t this ‘’directionality’’ simply the same directionality for all the numbers before \(\infty\)? In fact, that very much proves my point, and I hope some good discussion to arise from it.

[1] If 1 is the boundary of some finite point, then arguable, even though the example above moving from 1 to 207 then to infinity, which is simple 208, 209, 210 and so on and so on, still has a finite limit of 1, so there is absolutely nothing unique that can distinguish \(\lim_{x \to \infty}\) and \(\lim_{-\infty \to \infty}\).

 

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Doesn't make any sense.

Might I suggest you learn actual mathematical analysis before trying to make claims and tout your opinions? But then I've told you the same thing in regards to physics, never stopped you.

 

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I meant to say x to infinity.

Now with that explained, would you perhaps like to comment on my suggestions.

 

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But then again, that was pretty fucking obvious i meant x to infinity.

 

Saxion, do you know what the mathematical statement

\( \lim_{n\rightarrow \infty} \frac{1}{n} = 0\)

actually means? Your post suggests you don't.

 

I love it

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What's the other letter you use for a boundary, the Greek letter Alpha?

 

Did you mean x here, too?

 

Let me guess.

As n gets nearer to infinity, 1/n gets nearer to 0, to such an extent that if you could get n a shade away from infinity, 1/n would be a shade over 0.

The graph of 1/x shows this as it is asymptotic about y=0

I'm not very good at explaining, but I think I get it.

 

That's certainly not a bad guess, Steve100, although I'm dubious of your "the graph shows" bit - the graph only shows what you tell it to!

The actual meaning of the statement I posted is:

For each \(\epsilon >0\), \(\exists N\) such that for \(n>N\) we have \(|1/n - 0 |<\epsilon\).

This is, quite literally, what it means to say \(\lim_{n\rightarrow \infty} 1/n = 0\).

 

What do you think I'm going to say? I have already said that given your almost naivety about analysis in mathematics, ie the rigorous development and justification of mathematical methods, concepts and results, I find your suggests either pointless, incorrect and meaningless.

If you bothered to learn mathematical analysis you'd find that things 'going to infinity' or anything else which requires considering limits of unbounded quantities (such as Riemann integration) are all structured and justified. The problem is not with the maths but with the thing between your ears.

QuarkHead has started a few threads saying things like "Why I don't like Dirac bra-ket notation" and then giving an indepth, detailed and informed discussion about the mathematical rigorous way of working with Hilbert spaces compared to the perhaps more 'fly by the seat of your pants' method some of us physicists tend to use it for. He shows he's read about the topic, digested it and formed a coherent line of thought on the matter. You show none of those things. I highly recommend Burkhill's 'A First Course in Analysis'. It's pretty cheap and accessible to anyone competent at A Level mathematics, namely basis algebra, calculus and set theory. Unfortunately I don't think you meet that criteria so you might have to start with something a little more basic before even moving on to analysis.

Given you, more than once, said things like \(-\infty \to \infty\) it was not obvious because none of us give you the benefit of the doubt that maybe you did just make a typo. When you make the same kind of 'typo' several times in a post on a topic you don't seem to know about, the logical conclusion is that the typo is not an actual typo but you showing you don't understand. You even typed it out in words, "If 1 can approach infinity". Given you use the numeral '1' and not the word 'one' you can't even say you were using 'one' to refer to 'One's self', like a royal might (ie in the same manner as a sentence like "One feels like you don't know what you're talking about", like the royal 'we').

 

Sorry to say I don't actually know what your explanation means.
I've never even been taught what \(\lim_{n\rightarrow \infty} 1/n = 0\) type things mean, I just took a guess by looking at what has been said in different places I've seen such things pop up.

I understand what you mean about the graph though.

 

The gistof it is as follows: \(a_n \rightarrow a\) means that if you give me any number \(\epsilon>0\), no matter how small, all but finitely many of the \(a_n\) are within \(\epsilon\) of the limit \(a\).

 

I think I get you.

Thanks.

 

Of course. Shall i example it, because this mearly is here because to show i hate the term, approaching infinity.

 

Actually, after one mistake, i simply copied and pasted. That's why.

 

By the way, maybe i should have stated \([\infty, -\infty] x [\infty, -\infty]\), alphanumeric, instead of \(-\infty \to \infty\), for an infinitely large plane? Then maybe you would have been so critical with the work.

 

Steve, the graph Guest speaks of is the y-axis graph.

 

Please don't lie - it makes you look stupid.

 

Lie? It's very simple. In the limit, we say as \(a_n\) approaches 0, \(n\) tends to infinity.

So where did i lie?

 

Your grasp of mathematics is staggeringly low. To suggest you understand the definition of a limit, given your opening post and previous performances, is laughable.

You are making a fool of yourself.