Is 0.99 =1????

What would you say if I said that 0.999… (Also written 0.\bar{9}or0.\dot{9}) is equal to one? NO! Obviously… since we think that let there be any number of 9’s after the decimal, its still infinitesimally smaller than 1. That’s what I thought out loud when I first saw this article. But the weird thing is that there exists not one but numerous proofs of varying difficulties proving the above fact that indeed they are equal if we take into account Real Number System i.e., the normal numbers we use for the mathematically challenged.

Proof by Fractions:
Algebraic Proof:

The proof which is so obvious is based on a few basic assumptions of Real Numbers but they are assumptions anyways. Any one of those assumptions have to be undermined to make this equality void.

For A more lucid account see Wikipedia’s Featured Article on 0.999…


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