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Re: Non-Euclidean Arithmetic
Posted:
Sep 21, 2012 12:35 PM
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On Thu, Sep 20, 2012 at 12:40 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
> Paul Tanner II says:
>>You are again trying to limit what a term can mean, when you say that we cannot multiply any two real numbers.
>
> A completely absurd claim on your part Paul.
It is not absurd - it is what you said.
I will hold you to your own words.
In your post
http://mathforum.org/kb/message.jspa?messageID=7892884
you said in reply to me, and I quote:
">Repeated addition can compute products only if the products are computable - and since almost all real numbers are noncomputable, almost all real
> number multiplication is not computable.
>
Is it possible you are getting somewhere Paul? That's exactly right. Neither you, nor Devlin, can multiply two real numbers in general. You can't use a "scaling process" to do so, nor can you do so through "repeated adamant insistance.
You can assert the product exists, but that's a different game."
> I'd say its you who have trouble seeing things more than one way.
>
Your above words show that what you just said applies to you.
That is, you are in fact saying that we can multiply two numbers if but only if we can compute their product. I said that "almost all real number multiplication is not computable" which means that it is not the case that we can compute the product of any two real numbers. And you said in reply, "Neither you, nor Devlin, can multiply two real numbers in general."
> I'm simply pointing out the very *elementary* fact that multiplication on integers, and multiplication on real numbers, are not the same, in fact, worlds apart by some measures.
>
You are not *simply* doing this. You are going way beyond this and claiming that again, your words, "Neither you, nor Devlin, can multiply two real numbers in general."
As I pointed out in my post
http://mathforum.org/kb/message.jspa?messageID=7893419
we most certainly can multiply two real numbers in general.
And it is as I said in that post:
"You still seem to argue as if the models *are* what they model. I and he are trying to get people to see that this is not true, regardless of the model, scaling and repeated addition included, and regardless of whether whether the model is one in which we can compute."
That is, your own words, "Neither you, nor Devlin, can multiply two real numbers in general" say that you believe that we can multiply two numbers or elements of a set in general if and only if we can compute their product.
Again: I will hold you to your own words.
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