To add to what Kabi said, IIRC only when you’re speaking in set or groups do the infinities become “larger” (simplified and not 100% accurate). I.E. infinity of regular numbers vs infinity containing all the variations of positive integers added. The latter would be “larger” cause it contains multiple infinities or “sets” of infinities and is infinite within itself. This video helps explain probably better
Sure, “-∞ < ∞” is a useful concept, but it is not the same thing as when we talk about the sizes of infinities. What we mean by that is how many numbers it contains: (1,2,3,4…) contains fewer numbers than (1.0,…,1.1,…,1.5,…,2.0,…,2.5,…), but how large the actual numbers are, doesn’t matter. The second example contains just as many numbers, is just as “large”, as (1.0,…,2.0).
edit: Sorry for the snarky tone, I was going for nerd maths boy. Hope I at least am technically correct.
But there are infinities which are larger and smaller than other infinities.
-infinity is smaller than +infinity for the most simple example.
To add to what Kabi said, IIRC only when you’re speaking in set or groups do the infinities become “larger” (simplified and not 100% accurate). I.E. infinity of regular numbers vs infinity containing all the variations of positive integers added. The latter would be “larger” cause it contains multiple infinities or “sets” of infinities and is infinite within itself. This video helps explain probably better
https://youtu.be/dEOBDIyz0BU?si=cSCI969q7Aq-wsHo
Sure, “-∞ < ∞” is a useful concept, but it is not the same thing as when we talk about the sizes of infinities. What we mean by that is how many numbers it contains: (1,2,3,4…) contains fewer numbers than (1.0,…,1.1,…,1.5,…,2.0,…,2.5,…), but how large the actual numbers are, doesn’t matter. The second example contains just as many numbers, is just as “large”, as (1.0,…,2.0).
edit: Sorry for the snarky tone, I was going for nerd maths boy. Hope I at least am technically correct.
Yeah, I was going for simple rather than correct. I didn’t want to get into explaining Cantor’s Diagonalization to Lemmy folk.