Tuesday, October 9, 2007

Mathematics and Mysticism

ok so i have been spending a fairly long time on the net and thus came across this great unsolved mathematical mystery.!!!well thats wat they say!!
which is the smallest number greater than zero?
unsolved heh?ok so lets give it a shot!There is no "smallest number greater than 0". This is not only because Mathematicians are self-centred egotists, or even because maths profs are Mathematicians who wish only to flunk their students. Mathematics believes in doing well-defined things (ONLY). It's practically the science of well-defined things. Having a smallest positive number would break this. For suppose such a number x existed. Then we know x > 0, so x > x/2 > 0, which is a contradiction (x/2 is now smaller positive number!duh!!).
So no such thing exists. And you cannot meaningfully "define" something to be this nothing. There is no number 1/infinity, no number 1/aleph0, no number 1/ω, and no number 0.00...001 (where there are "infinitely many" 0's between the decimal point and the 1). None of them make sense, none of them are defined, and all of them are even more nonsensical than the idea of a smallest positive number x as above. And don't get me started on 0.99999...; it really does equal 1 (and no, 1-0.999... is not the "smallest number greater than 0").
Grow up; deal with it; there are bigger things to worry about.

PS-
-hey, what's the smallest number greater than zero?
>think of a number greater than zero.
-is this like a magic trick?
>in a way, yes.cool!
-i like magic tricks! alright, got one!
>halve it
-uhuh
>halve it again
-yup
>halve it again
-ok...

*** several minutes later ***
>halve it again
-um, how long is this going to take?

*** several hours later ***
>halve it again
-are you following me?!?!??!

*** several weeks later ***
>halve it again
-please! i can't take it anymore! can't we just call it quits and round it down to zero?!?!?!
>certainly not! halve it again...
-arghhhhhhh!!!!!!