Off Topic > Off Topic
the ultimate question: does 0.9999... equal 1
SetGaming:
--- Quote from: TableSalt on March 18, 2017, 08:13:15 PM ---Okay, so is this
0.999... (infinite 9s here) ...999
or is it
0.999... (infinite 9s here, with no literal end)
--- End quote ---
literal no end
Blockomaniac:
nerds
Shift Kitty:
Here's an idea...
Let's get rid of the decimal system.
Ipquarx:
In the set of real numbers, 0.9999... = 1.
In the set of hyperreals where you can have numbers infinitely close to but not equal to 1, 0.999... is not a valid representation of a number as far as I'm aware.
So yes, it's equal.
If you want some ideas of why, here are a couple proofs:
x = 0.9999...
10x = 9.9999...
10x - x = 9.0
9x = 9
x = 1
1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333...
...
7/9 = 0.7777...
8/9 = 0.8888...
So 9/9 = 0.9999..., and 9/9 = 1.
Texan101:
Easy solution.
.999... - 1 = What?
0.000....
Never has a 1 or higher, so it gets simplified to 0.