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 $$\lim_{-\infty \to \infty}$$.
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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