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Mar
4
comment Does there exist a system such that the additive identity is non-zero?
@DanielV: A system with two-sided additive identities has only one; if x + 0_a = x and 0_b + x = x, then 0_a + 0_b = 0_a and 0_b, so 0_a = 0_b.
Feb
3
comment Is it faster to count to the infinite going one by one or two by two?
Infinity is not a real number, so why should the limit of two functions as they approach infinity equal their values at infinity? I might compare it to "does the sequence 1, 2, 3 ... reach 133 faster then the sequence 2, 4, 6 ...?" The limit gets the wrong answer because only one sequence ever gets there; why should it work when neither gets there in finite time?
Nov
12
awarded  Supporter
Oct
17
comment Why is “the set of all sets” a paradox?
I don't see how you could not consider Quine's New Foundations a set theory; it has the usual universe of sets in it. It may in fact have a superset (superclass?) of ZF's sets, though it's possible stratified comprehension excludes some sets ZF includes. It is akin to NBG set theory; some definite weirdness if you're used to ZFC, but basically the same thing for practical purposes.
Jul
30
awarded  Analytical