A recurring argument with one of my friends and myself is about a mathematical truth namely that 0.999… = 1. It’s an interesting concept which took me a while to grasp. To convince yourself have a look at these two proofs,
Proof 1 – Fraction Proof
1/9 = 0.111…
Multiplying both sides by 9,
9*(1/9) = 9*0.111…
9/9 = 0.999
1 = 0.999
Proof 2 – Algebra Proof
x = 0.999…
10x = 9.999…
subtracting x from both sides
10x – x = 9.999… – 0.999
9x = 9
x = 1
For more proofs check out the wikipedia entry.
