0.9999... equals 1.0000....

[UltraBudgie]

numbers that repeat to infinity are weird.  let x equal 0.9999...

x = 0.9999...

then multiply each side by 10:

10x = (10 * 0.9999...)
10x = 9.9999...

then subtract x from each side:

(10x - x) = (9.9999... - x)
9x = (9.9999... - 0.9999...)
9x = 9.0000...

then divide each side by 9:

(9x / 9) = (9.0000... / 9)
x = 1.0000...

therefore 0.9999... = 1.0000...