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Cantor\"s set of Countable infinite and Uncountable unlimited Infinites

You may know and you may have actually proved that collection of actual Numbers between 0 and 1 space Uncountably Infinite.Mean we have the right to not Map Every number of that collection on a various Natural Number.

I gained a method by which i would have the ability to Map all actual numbers in between 0 and also 1 on a different Natural Number.Technique is basic Replace the Decimal suggest with 1 and also Map the initial on that Number Such that Map 0.0003 top top 10003 and also 0.03 on 103

By using this technique we Would be able to Map all actual Numbers between 0 and 1 on herbal Numbers. And every one of those organic Numbers will certainly be beginning with 1 for this reason we will be having other Numbers also on i m sorry No Number will certainly be mapped like2 or 211 or 79So This means Set of natural Numbers is Grater then actual Numbers between 0 and also 1. So set of actual Numbers in between 0 and also 1is Countably Infinite.

What\"s Ur Opinion ?

math collection infinite set-theory countable
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edited Oct 8 \"13 at 17:32

David Robinson
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asked Oct 8 \"13 in ~ 17:26

Ayub KhanAyub khan
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The set of real numbers in between 0 and 1 is uncountably infinite, as displayed by Cantor\"s diagonal argument which friend are acquainted with.

What may be surprising to girlfriend is the the set of reasonable numbers in between 0 and also 1 is countably infinite. The is, over there is a 1-to-1 correspondence between the integers and also all fractions and also numbers v a finite decimal expansion. Girlfriend can discover the evidence here.

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reply Oct 8 \"13 in ~ 20:54

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This doesn\"t work due to the fact that an arbitrarily non-rational actual number such together 0.5123129421... Is a legitimate real number yet the number 15123129421... Isn\"t. In the situation of the former, girlfriend can point out (at the very least in principle) wherein along the number heat it would certainly lie, however for the latter, it\"s impossible. Try to say the end 15123129421... Together one number (like 1022 is one thousand and also twenty two). Girlfriend won\"t it is in able to, because such number is no a herbal number.

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reply Apr 6 \"17 in ~ 20:56

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