Perhaps a refresher in real numbers would be useful.

Perhaps widdle this question down. Does pi exist?

The area of a circle is pi r^2. So, you can never really accurately figure out exactly what pi is so you really can’t figure out the area of a circle. But….. you can fill a circle and measure the area, no?

So, again, does pi exist even though you can’t completely tell anyone how much it is or even write it down. We are forever away from really knowing pi.

No?

There are infinitely many numbers like pi. Perhaps these are useful fictions.

Does it matter?

It depends on your world view.

Consider it and get back to me. Or, ignore it and move on.

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on July 24, 2008 at 7:03 am |The Infinity Problem « A New Kind of Science Blog[…] 24, 2008 by TheNKSBlogTeam This began as a comment on Russell’s post, “Do Real Numbers Exist?” over at Social Mode, and got a bit lengthy, so I decided to post it […]

on July 26, 2008 at 7:30 am |What Is Mathematics - the follow up to Do Real Numbers Exist « Social Mode[…] July 26, 2008 by un1crom A couple of posts ago I asked if real numbers exist (like pi). […]

on August 7, 2011 at 1:56 pm |John GabrielThere is no such thing as a real number. There is only an incommensurable magnitude which has come to be known as an irrational number. The rational numbers and incommensurable magnitudes (which can be approximated using rational numbers) have come to be known as real numbers. In truth, real numbers have never been well-defined because an irrational number has never been well-defined. Since the Ancient Greeks invented numbers, there has been zero progress in this regard.

Neither Cauchy sequences nor Dedekind cuts define a real number but these are still taught ubiquitously in universities worldwide.