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

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Taber McFarlin

Posts: 2
From: United States
Registered: 3/4/13
Re: How does infinitesimal exist?
Posted: Mar 5, 2013 6:54 PM
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That's what I had always thought, until I saw a few proofs that seemed to say otherwise! Here's one:

x = 0.999...
10x = 9.999... (Multiply by ten)
9x = 9 (Subtracts 0.999...)
x = 1 = 0.999... (Divides by 9!)

So this is where I see a weird problem! Today, though, I was thinking and though that when you multiply by ten, aren't there infinity - 1 nines after the decimal? That would make 9x = 8.9999...1 and x = (...Works it out on calculator) 0.999.... Oh so... wait what XD ! I guess I kind of just figured that out on my own!

But am I right in saying there are infinity - 1 nines after the decimal?

And now I'm confused about another thing. How can 0.999..., a rational number, be represented as a fraction?! 9/9 is 1 but anything over 9 is supposed to be that number repeating, (after the decimal place).

...Help?



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