Post ATjsHgB7WIkWFJxsmG by enigmatico@mk.absturztau.be
(DIR) More posts by enigmatico@mk.absturztau.be
(DIR) Post #ATiNynA88biUcbcTVg by enigmatico@mk.absturztau.be
2023-03-17T18:29:41.552Z
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I just read in a suppossedly "scientific" magazine article a mention of "infinity" as a number. And as a full fledged nerd, I am disappointed.As a concept, it simbolizes something that has no end. But in mathemtics, Infinity is not a number. It only simbolizes a very large number, but undetermined.For instance, when you take the limit of a function and it goes to infinity, or when a series diverge to infinity, its a way of saying the result becomes larger as some variable also becomes larger. How large, exactly? It cant be determined, because it has no limit.If infinity was a defined number, how would you qualify it? How can it be quantified? There is no way to tell, right? And thats why infinity is not a number, its just a concept.
(DIR) Post #ATiQ4UJjJgDVouxBLM by enigmatico@mk.absturztau.be
2023-03-17T18:53:06.886Z
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There is, however, a positive infinity, and a negative infinity. How do we know if it is positive or negative, if I said that infinity is not a number?Well, that's simple. I said that infinity is just a very large number, just undetermined. But we still know if it is positive or not through the rules of positivity of a number.For a number to be positive, it has to follow two rules. One, it's obviously bigger than zero. And the other one, if you add it with itself, you get a more positive value. And the same works for negative numbers, but in reverse. They are less than 0, and adding them by themselves result in an even lower number.Imagine we take any number. If you add it to itself and it gets more positive then its a positive, as long as it is lies in the right side of the geometric representation. Can infinity be positive infinity? Yeah! If it is a large value greater than 0 and adding it or any other positive value would yield an even bigger value, we say its positive. And the exact opposite for negative infinity.But what if there is a positive and a negative infinity? Well, then we'd have to figure out, if possible, which positive grows faster to infinity. The one that grows faster is where the result diverges to. Of course, both could grow at the exact same rate and be exact opposites, at which point the result converges to zero, or minus one if dividing each other.
(DIR) Post #ATjsHfTs769e5BjLMm by ryedai@mastodon.social
2023-03-18T10:29:15Z
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@enigmatico Isn't Infinity-1 also an infinity ?Aren't there "multiple" infinities ?
(DIR) Post #ATjsHgB7WIkWFJxsmG by enigmatico@mk.absturztau.be
2023-03-18T11:43:56.480Z
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@ryedai@mastodon.social Infinity-1 means it grows a little bit slower than just infinity. Picture it like that.But in mathematical terms, infinity-1 is just infinity.There arent multiple infinities, there are numbers that grow at a faster rate and numbers that grow at a lower rate. Or the opposite.
(DIR) Post #AU1IPXsd1PA6R4UxZg by anedroid@mstdn.social
2023-03-26T21:18:44Z
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@enigmatico The proof of concept:There are three numbers - a, b and c like:|a - c| = k |a - b| and a - b ≠ 0 and k > 0Now, how many real numbers are in set <a, c>? The infinity. In <a, b> too. But infinity of the count of numbers in <a, c> are the count of numbers in <a, b> times k. We couldn't refer to the infinity without referring to its source to be precise, just like we can't describe an irrational number as just fraction of two integers.
(DIR) Post #AU1IPYaaNyK8dP445g by anedroid@mstdn.social
2023-03-26T21:26:24Z
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@enigmatico In geometry we face this problem everywhere: there is infinite amount of points in a line, infinite amount of lines in a flat figure, infinite amount of surfaces in a solid and so on, and rarely one infinite is equal to another. Because math does not explain the conception of infinity well enough, we always assume a number cannot be divided by zero. Formerly we hadn't believed in roots of negatives and even before in irrational numbers. Perhaps that will change too.
(DIR) Post #AU1JLGRlznG9ACSY6a by anedroid@mstdn.social
2023-03-26T21:37:14Z
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@enigmatico In wheel theory multiplying by zero not always equals zero. If k = a/0, then obviously 0k = a.https://en.wikipedia.org/wiki/Wheel_theoryhttps://vid.puffyan.us/watch?v=ydLTfyXaQmUBut it's controversial and not adopted to the mainstream math until it's proven it does not conflict with the other concepts or these can be explained somewhat else, so there is a lot of work to do.
(DIR) Post #AU1KWvvoCJusxsdWTo by enigmatico@mk.absturztau.be
2023-03-26T21:50:31.854Z
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@anedroid@mstdn.social There is a lot of ways to prove it, although the concept of infinity is relatively "new" in history and has been subject to changes throughout history. For instance, take a simple sequence like\{a_n\}^{+\infty}_{n=0}So the sequence is strictly increasing and strictly monotone, and it goes like1,2,3,4,5,...,a_n,...If this sequence had an 'end' and wasn't infinite, there would be an upper bound M whose value is greater or equal than the value of any of the terms in the sequence. That is, a_n \leq M. That is, it would be bounded by an upper limit and it would converge to that limit M.But this isn't the case. As n increases, so does the value of the nth term a_n. Therefore there is no upper limit M that is greater or equal than every nth term of the sequence. So it is not bounded and it diverges.This divergence is what makes it "diverge to (positive) infinity". And the opposite works for negative numbers as well. No matter of what number you think of this sequence, there will always be a bigger term.This is what most people understands for "infinity" in mathematics. You take a value, and then analyze what happens when that value grows larger and larger, either in the positive or the negative side.Naturally there are more kinds of "infinity" that are not strictly attached to this definition, like having an infinite number of divisions in a line, having an infinite number of decimals (which still converges to a limit as a number, as there is an upper and lower limit), etc etc. But generally speaking, this is how it is supposed to be interpreted.
(DIR) Post #AU1LhwSEh37pj6cKOG by enigmatico@mk.absturztau.be
2023-03-26T22:03:43.979Z
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@anedroid@mstdn.social Well, maybe that will become a special case like complex numbers and complex analysis, where the square root of a negative number is defined. Why not :akko_shrug:The fact that the division by zero is not defined is because any function that has a division has no limit when the denominator approaches zero. The limit from the left is negative infinity and the limit from the right is positive infinity. And because it has no limit, we can't say it's defined at that point.But so are square roots of negative numbers, so there might be a special case where it can be defined, sure.