Some responses

Here are responses that appeared on my Facebook account. Apparently one can synchronize her blog with facebook. Good for getting feedbacks.

Eray Ozkural at 5:48pm February 16

sqrt(2), an irrational number, is also a computable real (a real number that can be represented by a simple approximation procedure). such numbers are realized only by computation, i.e. they are still idealization. in other words, you can write an _exact_ computer program that will churn out digits of sqrt(2). that is the best kind of realization you can hope in analysis in general. see weihrauch's textbook: http://eccc.hpi-web.de/eccc-local/ECCC-Books/klaus_book_readme.html

that is to say, the concept of triangle is a computable one. so, it is something that you can conceive of without any loss of conceptual clarity since our minds are computers. this criterion of complete conceivability does not apply to uncountable sets, for instance.

in real life, therefore, it is sufficient to use only R_c and forgo uncomputable numbers. the computability simply allows us to approximate real life situations to the best of our computational ability. sqrt(2) thus represents a limit.

Onur Gun at 6:46pm February 16

in real life everything is approximation, there is no exact sqrt(2) neither 1, i.e. if you draw a side length 1 it is going to be very close to 1. Anyway, I think that is related to quantum mechanics where the idea is you cannot measure things without perturbing the system...

Eray Ozkural at 8:31pm February 16

that usually implies a discrete system, so it's related to the idea of computation

Thank's for the responses will get back to them shortly, now I have to catch a class, in a cold snowy day.