Prove that 3.999... = 4

Gamer, you apparently aren't convinced. Here's yet another proof for you:

Imagine the function f(x)=4-1/(10^x).
The line would be 3.9999..., where x is the number of 9s, right? Well, as x approaches infinite, f(x) approaches 4. So 3.999... with infinite nines is 4. You'll probably disagree with this still, and I myself admit there might be a problem somewhere.

To adress your other doubts, the fact that two different numbers have more numbers inbetween on the number plane I think is a postulate. If you want to go questioning postulates, than maybe the reflexive property is false as well, and 4 doesn't equal 4.

On dividing by 0 or infinite, I think those count as postulates as well. I think you know why people think we can't divide by zero. You might say we actually can. If you graph all the points where x/0=y is true (not really a function), then you will get the y-axis. x/0 can equal anything, then. But this has its limits, or you would be able to prove 1=0, and 3.9=4. As for infinite, ∞+1=∞. Infinite is the highest you can go by definition.

If you're actually just trying to make us think or something to that effect, well good job then. Keep it up and I'll have to make up a dozen more proofs.

Edited on November 16, 2003, 3:49 pm
Edited on November 16, 2003, 3:51 pm

Posted by Tristan on 2003-11-16 15:47:57