Re: Idle Thoughts

Nick Hodges [TeamB] wrote:
> paladin wrote:
>
>> there is a simple proof to show that 3.99999... (repeating forever)
>> is *the same* as 4.0
>
> What does "the same as" mean in mathematics?

Exactly what you think it does. ;-)
What probably is confusing is the notation of a limit, what 3.9999... really
means.

Call Delta the difference between 4 and 99999...
that is, Delta:= 4 - 3.9999.....

If Delta > 0, you must have "cheated", "stopped the 9s" somewhere. This is
because 3.9999... can get as close to 4 as you want, closer than any given
Delta.
So Delta = 0, meaning that 4 and 3.9999.... is the same number.

Cheers,
Jarle


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