Re: Idle Thoughts

Bob Dawson wrote:
> "Jarle Stabell" wrote
>>
>> (This proof-technique, starting with the opposite assumption
>> and trying to end up with something known to be false, is
>> called reductio ad absurdum)
>
> And doesn't work in areas like infinity.
> For example, if we can
> conceive of infinity + 1,

Search for ordinal arithmetic and you will immediately find the common
definitions of how to add and multiple infinite ordinals...

Historically, some groups didn't buy into reductio ad absurdum as a valid
proof-technique, but I believe the current researchers in Constructive
Mathematics are into it because are interested in whether one can find some
new useful practical (typically computer related) techniques by removing
that weapon from the arsenal, not because they have a philosophical problem
with reductio ad absurdum.


> then does that prove that infinity isn't
> infinite? Challenging someone to find a workable value for the delta
> is simply inviting them into a mathematical trap,

Why? It is an extremly common and useful technique.

Cheers,
Jarle
--
"Reductio ad absurdum, which Euclid loved so much, is one of a
mathematician's finest weapons. It is a far finer gambit than any chess
gambit: a chess player may offer the sacrifice of a pawn or even a piece,
but a mathematician offers the game" [G. H. Hardy]


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