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Anonymous at Tue, 2 Jul 2024 08:11:55 UTC No. 16264027
>there are infinitely many natural numbers
This simple and trivial fact makes finitists piss and shit themselves. Their defective brains don't allow them to understand something that is obvious to any kid in elementary school.
pic related, the average finitist
Anonymous at Tue, 2 Jul 2024 09:05:35 UTC No. 16264086
>>16264027
OP is a retard. But let me stay on the topic: If Im on a measurable space and I want to show the measure of the infinite union of a sequence of sets is less than or equal to the sum of the measures, can I use induction?
Anonymous at Tue, 2 Jul 2024 09:10:06 UTC No. 16264088
>>16264086
For countable unions that's an axiom. Uncountable unions don't need to be measurable anymore. There, I did your homework for you. You can tip me on onlyfans.
Anonymous at Tue, 2 Jul 2024 09:41:12 UTC No. 16264124
>>16264086
No, induction would only prove the finite case.
Anonymous at Tue, 2 Jul 2024 10:01:40 UTC No. 16264140
>>16264124
whyyy goddamn it. I thought induction would already prove "for all n"
Anonymous at Tue, 2 Jul 2024 10:03:14 UTC No. 16264141
>>16264088
Only an axiom if the sequence is disjoint
Anonymous at Tue, 2 Jul 2024 10:42:02 UTC No. 16264169
>>16264141
>subadditive with equality if the union is disjoint
But you can of course choose other axioms since the equivalence is trivial unless you're a pajeet like >>16264086
Anonymous at Tue, 2 Jul 2024 11:05:24 UTC No. 16264186
>>16264140
For all n means that every finite case is true, not that the infinite case is true.
Anonymous at Tue, 2 Jul 2024 11:23:29 UTC No. 16264200
>>16264169
Why does everyone assume I'm a pajeet