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

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mathCurious

Posts: 9
Registered: 4/29/13
Re: RE: How does infinitesimal exist?
Posted: Apr 30, 2013 8:12 PM
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So I just want to make sure I have this straight. You are telling me that on (0,1) you have aleph-nought rationals and that on (0.5,0.75) you also have aleph-nought rationals.

Am I correct in thinking then that the intersection of the rationals contained on the intervals (0,1) and (0.5,0.75), when regarded as being seperately "infinitely divided" into rationals, would have a smaller cardinality than aleph-nought, but still be infinite? This seems like a contradiction, so it confuses me. Am I making some logic mistake somewhere, or is there some concept that covers this which I am clearly unaware of? Thanks a bunch for answering.

I looked up cardinal number and I get aleph-nought, but what specifically they mean by aleph-one, aleph-two, etc. confuses me.



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