## AmTran_Bus 3 years ago Prove .99999999999999999999999999999999999999999999999999999 equals 1.

1. yummydum

that is false.....the number mentioned above ROUNDS UP to 1....meaning it is closer to one than it is to 0 :)

2. AmTran_Bus

Good job! Now try .9 repeating!

3. yummydum

its the exact same explanation thou stubborn being

4. asnaseer

If you mean 0.999... (i.e. 9's repeating for ever) then this can be proved

5. AmTran_Bus

Go fir it!

6. asnaseer

is this a challenge or are you looking for help in trying to prove it?

7. AmTran_Bus

I want to prove it.

8. asnaseer

ok, start by setting:\[x=0.999..\]Then see what happens if you multiply both sides by 10

9. AmTran_Bus

10x=0.999(10)

10. AmTran_Bus

or 9.999999999---

11. AmTran_Bus

10=9.99999999 on and on

12. asnaseer

correct - and now notice that 9.99... can be written as 9 + 0.999...

13. AmTran_Bus

right

14. asnaseer

and what is 0.999.... (look at how we started the proof)

15. AmTran_Bus

you mean =x?

16. asnaseer

perfect!

17. asnaseer

so you end up with: x = 0.999... 10x = 9.999... = 9 + 0.999... = 9 + x

18. AmTran_Bus

ohhhhh. Thanks!!!

19. asnaseer

yw :)

20. phi

how about x=0.9999... 10x= 9.9999... 10x-x = 9 9x=9 x=1

21. asnaseer

thats basically exactly what we have done :)

22. phi

yes, just wanted it all in one post for other readers