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# 0.999...=1 ?

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Does 0.9999.... =1 ? Prove it.

Jan 7, 2015

#2
+5

Perhaps not perfect proof, but I would do as follows:

x = 0.9999... |multiply both sides by 10

10x = 9.9999...

Now 10x - x = 9.9999... - 0.9999..., so

9x = 9,

Thus x = 1

Jan 7, 2015

#1
+94976
+5

This is not a formal proof, it is more of a demonstrations

You can show by division that                       $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$   = 0.3  repeater.

If you multiply both sides by 3 you get           $${\frac{{\mathtt{3}}}{{\mathtt{3}}}}$$   = 0.9 repeater

but     $${\frac{{\mathtt{3}}}{{\mathtt{3}}}}$$  = 1       so

1 = 0.9 repeater

Jan 7, 2015
#2
+5

Perhaps not perfect proof, but I would do as follows:

x = 0.9999... |multiply both sides by 10

10x = 9.9999...

Now 10x - x = 9.9999... - 0.9999..., so

9x = 9,

Thus x = 1

Guest Jan 7, 2015