Quote:
Originally Posted by ZenGum
Think of the number line. Zero in the middle, negatives off to the left, positives off to the right. .9r would be immediately to the left of 1. We zoom in, closer and closer; .9r is always abutting 1 on 1's left, but never quite in the same place. Keep zooming, it is always there.
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How can you tell they're not in the same place? There's no space between them. No matter how much you zoom in, that space will never open up.
Quote:
0.9 < 1
0.99 < 1
0.999 < 1
0.9999 < 1
etc
0.999999999999999999999999999999999999999999999 < 1
Observation: adding more nines does not change the fact that it is less than one, no matter how many you add.
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Infinity is different. For example:
No matter how many finite numbers you add together, you will never reach infinity - unless you add an infinite number of numbers.
Likewise, no matter how many nines you add to 0.9999..., you will never reach one - unless you add an infinite number of nines.
Quote:
Originally Posted by Rhianne
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That's the page I tried to copy-and-paste the proper barred number from.