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CTK Exchange
alexb
Charter Member
2340 posts |
Mar-23-07, 04:53 PM (EST) |
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1. "RE: wisdom of calling irrational numbers real"
In response to message #0
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>At the URL
>https://www.cut-the-knot.org/do_you_know/numbers.shtml#deficient
>it'says,
>Ian Stewart questions the wisdom of calling irrational
>numbers real: How can things be real if you can't even write
>them down fully?
>
>Does this mean that he concedes that integers are real? I can't talk for Ian Stewart, but I'd think his sentiment is not uncommon. Most recently I came through the same notions but in a more rigorous form in N. Wildberger's Divine Proportions. > If
> he does what is real about 1, 2, ...? I do not know. On the other hand, John Conway and Richard Guy claim complex numbers to be real while real numbers are simple.
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kate
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Mar-11-09, 04:28 PM (EST) |
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2. "RE: wisdom of calling irrational numbers real"
In response to message #0
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I can write down irrational numbers fully. Example, use the square root sign and put a 2 under it. There, it's fully represented. Just because it's in base 10 doesn't mean it's not able to be represented fully in another base. |
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alexb
Charter Member
2340 posts |
Mar-11-09, 04:35 PM (EST) |
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3. "RE: wisdom of calling irrational numbers real"
In response to message #2
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You can name the number, yes. π is a number. Sure. > Just because it's in base 10 doesn't
> mean it's not able to be represented
> fully in another base. Rational number may have finite or infinite expansion depending on the base, e.g. 1/3 = (.1)3 and
1/3 = (.333...)10 If we consider only integer bases then irrational numbers have infinite expansions regardless of the base. |
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