I've been called a workaholic. I'm pretty much always working when I'm not drinking. --Brehnen Keilin

A True Math Nerd In An Otherwise Completely Normal Conversation

First Posted: June 6, 2015, 11:01 a.m. CST
Last Updated: June 25, 2015, 5:20 p.m. CST


Copied and pasted by Brehnen Keilin

John
You wanna know what's weird? We will both be 32 in two days.

Brehnen Fri, 8:52 PM
that's a weird coincidence!

John • Fri, 8:53 PM
i know! only happens once if two individuals are less than a year apart in age

Brehnen Fri, 9:23 PM
Topologically speaking you are correct. If the number of times that we can be said to both have the same age is the measure of the set of absolute time during which we can be said to have the same age, then the measure can be interpreted in a few ways. If the measure is the lebesgue measure, then the continuous time interval gives us the distance between our birthdates. But if the measure is the cardinality of the set of partitions or possible arbitrary partitions, then the "number" is the cardinality of the borel sigma algebra, since a dense space of the real numbers can be partitioned into one space, two spaces, several spaces, any finite number of spaces, any countably infinite number of spaces, and an uncountably infinite number of spaces consistent with the cardinality of the borel sigma algebra. But then there is the question of whether the number of partitions is equal to the number of arbitrary partitions that DOES occur, or the number of partitions that CAN occur. However, if the measure is equal to the number of connected topological spaces during which we can be said to have the same age, then the answer is 1. The single interval of continuous time cannot be constructed from a union of disjoint open sets.



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