@ughaibu,
ughaibu;171899 wrote:I dont see how you can get real numbers this way. You describe yourself as some kind of intuitionist, do you only accept computable real numbers?
I think we view all numbers as unities, really, even complex numbers. If we look at irrational numbers, we can see them as algorithms for the calculation of rational numbers. Pi and e exist either as rational approximations or as our unified conception of them as a way to get these approximations. This is why I find transcendental and/or irrational numbers so fascinating. They push the limits of the number concept.
But yes I argue that concept is
essentially finite. But our sense of space is continuous. So the number line contains an uncountable infinity of points/numbers, precisely for this reason. We can imagine spatially infinite precision. But we only clearly
conceive (count) finite and precise magnitudes. And these magnitudes are modifications of the unit. It's all about the clash of the continuous and the discrete, in my mind.
I offer this humbly. It clicks for me, but maybe not for others.