Aug 19, 2026 · 27 min · 10 segments
What Is a Set? A Beginner’s Guide to Set Theory Your support helps us keep these conversations going! If you’d like to contribute, you can buy us a coffee here…
Thorsten AltenkirchHostDeniz SarikayaHostI think, uh, sets, uh, or the idea of c- of, of like collection is quite old.
I mean, you talk about like the real numbers, the integers, and the groups, and so I think this is quite, uh, old.
People talked about this, but they didn't, they didn't view sets as mathematical objects.
Um, but, uh, this changed, and I think the, the main person who, who, who, who, who changed this was, uh, was, uh, Cantor, uh, who, who, who, who started to consider sets as mathematical objects and, um, and, uh, and, and like that, that you can talk about sets like you talk about numbers.
Uh, if you have the property being green, then you can form the set of all green things.
this is like an interesting quirk of mathematics and foundations in general, that we take these meta notions and bring them into our very own theory.
Right? It's the same with proof theory, and in particular, if we have like limit results, there couldn't be a proof of something, n-not because it's wrong, but because it's independent or something like that.
There you need to make things precise, right? You cannot wave around and say, "Oh, this is independent," but you really need a notion of proof, a notion of model, of whatever.
And for the history of set theory, I mean, I'm no expert there, uh, but Cantor is often discussed as the-
I think, uh, sets, uh, or the idea of c- of, of like collection is quite old.
I mean, you talk about like the real numbers, the integers, and the groups, and so I think this is quite, uh, old.
People talked about this, but they didn't, they didn't view sets as mathematical objects.
Um, but, uh, this changed, and I think the, the main person who, who, who, who, who changed this was, uh, was, uh, Cantor, uh, who, who, who, who started to consider sets as mathematical objects and, um, and, uh, and, and like that, that you can talk about sets like you talk about numbers.
Uh, if you have the property being green, then you can form the set of all green things.
this is like an interesting quirk of mathematics and foundations in general, that we take these meta notions and bring them into our very own theory.
Right? It's the same with proof theory, and in particular, if we have like limit results, there couldn't be a proof of something, n-not because it's wrong, but because it's independent or something like that.
There you need to make things precise, right? You cannot wave around and say, "Oh, this is independent," but you really need a notion of proof, a notion of model, of whatever.
And for the history of set theory, I mean, I'm no expert there, uh, but Cantor is often discussed as the-
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