.999999.... = 1?

I was curious, My geometry teachers says that there's a theorm or theory or something that .99 repeating is acutally equal to 1. becuase it would become so small that it wouldn't matter. Is this true? At what point does the 0.00....00001 not matter anymore?

 

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here is a thread we had about that. the question is looked at from a million different angles there.

also, james answered this one just a few days ago here

 

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There is no point where .999... becomes 1. It's just a logical point where the difference between 1 and the repeating 9s could be safely ignored.

 

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0.9' is already 1.

just as where a greek person writes /\ (a triangle), i write teh word "delta"
a french person says "salut" i say "hello". we mean the same thing. 0.9' is an alternative representation of 1.

 

hey, here is a novel idea, why don t we start this thread all over anew? that will be productive. everyone, why don t you opine about the differences and similarities between 0.999 and 1.0.

huzzah for repetition!