If r is a random number between 0 and 1 then how do we model a coin flip?

The set of outcomes is {x >=0 & x<=1 & x in set of Reals}

I am blogging this because it is the same problem as boundaries before.

To split this set in half we cannot use a member of the set. So the obvious choice is 0.5 but what about 0.5? It is infinitely unlikely to occur in reality but never the less it sits there "outside" the sets.

The set {0,...,0.499...99} maps to {1 , ... , 0.50...01} or better the intervals

[0,0.5) (0.5,1]

This is an old problem that still gets me. When programming a for loop we need to set the condition to end. But what when counting through a string. Happily C style languages are 0 based so the following will work

for (int i=0; i < length(string); i++) {

//the length function returns the number of characters e.g. length("hello") = 5

//but conventionally the first character is in the 0th position

//and the last character in the 4 position so the loop above works

}

More obvious in a ruler where each interval has a start and ends with the start of the next interval until the final measurement which needs a final 'cap'. So there are one less intervals then measures. Hence the old problem that the millennium actually came at the end of the year 2000 not the start.

Now are these issues of boundaries connected? I'm in a hurry here not sure. I understand that this is still a real problem in some areas of topology.