0,999... = 1 - The easiest mathematical proof there is
Mathematical proofs normally have the problem of either being too trivial or too hard to understand to talk about them in day to day conversations. One exception is the 0.999...=1 proof, most people instinctively do not believe it to be true, yet it is very easy to prove:
1/3 = 0.3333... | x3
3/3 = 0.999...
since 3/3=1 our proof is done at this point. The only question is if it convinced you. There are different ways to approach this problem. A long but elegant one is looking for numbers between 0.999... and 1 to see that there are none and since this cannot be the case for 2 different numbers in the set of rational numbers 0.999... and 1 have to be the same number.
Do you believe me or did you already know and want me to do some more hardcore math proofs on my blog?
wow that is probably the fastest proof ever,
but what if it is instead proving 1/3 is not exactly 0.33333...
food for thought :)
well that is a fair criticism since I set 1/3 = 0.333... as being true without proving it. However proofing the looped nature of periodic numbers is not that hard, but to be formally correct you would have to take a function with a1b^1+...+anb^n with b = 10 and that is quite formal/complicated.
That sounds all very plausible what you are writing than I believe you;) But if you would write more of it, I would be happy too ;)
Also nur her damit ;))
That is simply a problem of popular tenth or whatever system it is called. I read once that when some mathematician found out that you get infite number by dividing 10 with 3, they tried to hide it. Think about face of that guy when he realizes his run out of the paper by writing number 3 over and over again.
Like many things in live, this is only a "problem" if you decide to see it as one.