Proof that .99 repeating = 1?
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timmy_i_chen (1011)

Can anyone help me find a proof that says .999 repeating is equal (no approximations) to 1? We got into a big discussion about this on Discord recently.

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pyelias (929)
.999999..
= 0.9 + 0.09 + 0.009 + ...
= 0.9 * (1 + 0.1 + 0.01 + 0.001 + ...)
= 0.9 * 1 / (1 - 0.1)
= 0.9 * 1 / 0.9
= 1