In <20120524143314.779$aq@newsreader.com>, on 05/24/2012 at 06:33 PM, curt@kcwc.com (Curt Welch) said:
>By declaring "infinity exists" as an axiom, it seems to me one >would be introducing a contradiction into their set of axioms
Mathematics is not about how it seems to you. Produce a contradiction if you can; until then no rational person will take your belief seriously.
>nonsensical hierarchy of infinities
The fact that you don't like it doesn't make it nonsensical.
>Has there been found any application in this universe where the >act of pretending infinity exists becomes useful?
Has there been found any application in this universe where the act of pretending numbers exist becomes useful? Like numbers, cardinals are abstractions. Theories using those abstractions have found practical use.
>But that can't exist.
Asserting that they can't exist doesn't mean that they don't.
>But there are processes that never end, and we can use any of >these processes as a definition.
Mathematics is not founded on a concept of processes.
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