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Math Forum » Discussions » Math Topics » discretemath

Topic: How does infinitesimal exist?
Replies: 21   Last Post: Jun 7, 2013 12:13 AM

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Peter Scales

Posts: 111
From: Australia
Registered: 4/3/05
Re: How does infinitesimal exist?
Posted: Mar 5, 2013 9:36 AM
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> 1 - 0.9 repeating is infinitesimal correct? However,
> if 0.9 repeating is equal to 1, which is proven,
> shouldn't it equal 0? I feel like these ideas
> conflict, how can this be?

Hi Taber,
Here's one suggestion:

I think you just have to use your imagination a bit.

0.9 repeating is not equal to 1 until you have put in the "last 9"! This is obvious, because, for any finite number of 9's we know, and can calculate, the difference (= delta).

As we get ever closer to that "last 9" delta gets smaller and smaller. In fact it becomes vanishingly small or smaller than any value you can think of.

When you get to the "second last 9" it will be really tiny! But it is still > 0

We say it is "infinitesimal".

Regards, Peter Scales.

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