### Comments

Let's have fun with unanswerable questions. Questions we can prove are unanswerable!

Do you ever write about anything that has to do with WORDS as opposed to MATH? My dad is a math person and my mom is a word person, so I like both.... *crickets chirping*..... Ok, how 'bout those unanswerable questions?

The coolest math fact ever is Thurston's geometrization conjecture/theorem.

elspi:

do you mean that the fact that i called the coolest follows from Thurston's theorem? or that you have a different opinion on the coolest?

either way, i admit that i don't know nearly enough math to understand the explanation of that theorem on wikipedia.

coolest math fact ever:
e^(pi*i)+1 = 0
proof time!

I'm a big fan of pathological functions myself. Fun little examples, like the function that's defined everywhere, but continuous at exactly one point (f(x)=x on the rationals, f(x)=0 on the irrationals).

For more advanced functional fun, there's the fact that most (!) continuous functions are not differentiable at any point, and the fact that there exist space-filling curves.

How about this:

If an integer, n, is divisible by neither 2 nor 5, that integer *must* divide a number of the form 10^m-1 (where m is a positive integer). I have no idea how to prove this except that, given that 1/n, a rational number, is expressible as a repeating decimal, it must be the case that 1/n = b/(10^m-1), where b is the integer value of the repeating sequence in the decimal, and m is the number of digits in that sequence. (Yes, I thought this up when contemplating 0.999...=1).

I really think there should be a cleaner proof.

Twinkle, that statement is special case of Euler's Theorem. Wikipedia has a nice proof, but it involves some group theory.

answer please.

for example you wanna buy something worth \$97.00, but you don't have money, so you borrow from you 2 friends \$50.00 each for a total of \$100.00. you still have change of \$3.00, you gave \$1.00 dollar to each of your friend whom you borrowed money from, that gives you 1 dollar left and a debt of 49 dollar from both of you friends. if you add, 49+49=98. plus the 1 dollar left with you. 99 in total. where did the other dollar goes?

of the three dollars, you subtracted two of them (50-1=49) but then added the last (98+1=99). you should subtract that last dollar, 98-1=97, and 97 was the cost of the item.

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