Re: Relative Cardinality



Jan de Vos wrote:
> In sci.math, mueckenh@xxxxxxxxxxxxxxxxx wrote:
> > But you believe that sqrt(2) is a number because 2 is a number. That is
> > too short sighted.
>
> Consider a triangle with a right angle, and two sides of equal length,
> 1. What is the length of the diagonal?

Is this triangle made of matter? Then euclidean geometry is disturbed.
It is hard to find the length of the diagonal. Is it only imagined?
Then the lengths of all sides are very uncertain, up to +/- 10 % I
would asuume.

> Does the length exist?

Of course. It is an idea. But we do not know whether it is a number.
Your triangle, made of ideal matter but in the limit of vanishing mass,
may have a diagonal which cannot be expressed by a number. So what?
Don't you know of things which ahve no expression by numbers? Taste,
feelings, beauty?

> If
> not, do you think this triangle exists at all?

Not this one, unless you have a special one in mind, but many triangles
do in fact exist. I am not a solipsist.

Regards, WM

.

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