this post was submitted on 27 Jun 2024
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2/9 = 0.222... 7/9 = 0.777...
0.222... + 0.777... = 0.999... 2/9 + 7/9 = 1
0.999... = 1
No, it equals 1.
Similarly, 1/3 = 0.3333…
So 3 times 1/3 = 0.9999… but also 3/3 = 1
Another nice one:
Let x = 0.9999… (multiply both sides by 10)
10x = 9.99999… (substitute 0.9999… = x)
10x = 9 + x (subtract x from both sides)
9x = 9 (divide both sides by 9)
x = 1
My favorite thing about this argument is that not only are you right, but you can prove it with math.
Not a proof, just wrong. In the "(substitute 0.9999… = x)" step, it was only done to one side, not both (the left side would've become 9.99999), therefore wrong.