Limits at infinity are one thing, but infinite ordinals are meaningfully used in set theory and logic
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Ephera@lemmy.ml â¨2⊠â¨months⊠agoOur mathematical definitions say that it does not end. Weâve defined addition so that any number + 1 is larger than that number (i.e. x+1 > x).
Youâre probably confused, because you think infinity is a concrete thing/number. Itâs not.
In actual higher-level maths, no one ever does calculations with infinity.
Rather, we say that if we insert an x into a formula, and then insert an x+1 instead, and then insert an x+2 instead, and were to continue that lots of times, how does the result change?
So, very simple example, this is our formula: 2*x
If we insert 1, the result is 2.
If we insert 2, the result is 4.
If we insert 82170394, the result is 164340788.
The concrete numbers donât matter, but we can say that as we increase x towards infinity, the result will also increase towards infinity.
(Itâs not 2*infinity, that doesnât make sense.)
Knowing such trends for larger numbers is relevant for certain use-cases, especially when the formula isnât quite as trivial.
kogasa@programming.dev â¨2⊠â¨months⊠ago
weker01@feddit.de â¨2⊠â¨months⊠ago
That is until you meet analysis people that define a symbol for infinity (and itâs negation) and add it to the real numbers to close the set.
Also there are applications in computer science where ordering stuff after the first infinite ordinal is important and useful.
Yea unfortunately we do kinda calculate with infinity as a concrete thing sometimes in higher level mathsâŚ