Ok, so Cecil did a pretty good job explaining why 0.999~=1, now I’m here to explain why it doesn’t
First, I’m gonna give you a little proof
If you multiply by 10
Subtract x from each…
9x=9 (because x=0.999~)
divide both by 9 to find x
However, there is one problem with that proof, and that is it treats infinity as if it is not an actual number. What we must remember is that infinity if a number, just a number we cannot express.
When we multiplied both sides by ten, it was 9.999continuing infinitely-1. In an equation, infinity must remain the same number, so multiplying by ten would remove a decimal at the end just like 0.99*10=9.9, NOT 9.99. Therefore, this argument is false.
Regarding fractions, 1/3 DOES NOT=0.333~. That is the best way we can put in it non-fractional form. The only true equal of 1/3 is 1/3. Saying 1/3=0.33~ is like saying 22/7=pi. It’s pretty damn close, but not quite right (perhaps the most accurate way of expressing 1/3 would be to say 0.333~+0.000~1, meaning that it ends in a four.)
Anyway I hope this has been helpful, and the original column can be found here . Now I just have to finish my explanation of Stairway to Heaven, last time the forum deleted it when I tried to post…