Let’s try again! In the context of this puzzle I believe I am
THE SET OF REAL NUMBERS
Title:
A lot of us non-mathematicians are familiar with the term REAL NUMBERS but often have misconceptions as to what they are.
Hints:
1)
This is pointing to the significance of the sound of queue.
The first two letters (AN, AL, TO) of the speakers names are clues which hints at different kinds of Mathematicians. They are an Analyst, Algebraist and Topologist respectively.
And so…
Anna says:
You have those I ask for size
Mathematicians ask for the size of the subsets within it. With the Lebesgue measure, the set of real numbers becomes a measure space, where subsets of are assigned a non-negative real number representing their size.
Though not (for) everything inside
Certain subsets cannot be asked for size because their size is not measurable.
Completing the order of queue
That's how I acquire you
Completing the ordered field of Q (set of rational numbers) you obtain the Set of Real Numbers - a Complete ordered field. This can be achieved though Dedekind Cuts.
Alex says:
Number of queues I cannot count
Joined to pose you, a new fount
This means to identify R as a vector space over Q.
Another copy of you
That's completion to go through
This is talking about the fact that another copy of R is needed for algebraic completion, to acquire C – the complex numbers.
Tommy says:
Already so complete (on its) own
No breakage when let alone
This is referring to complete metric space.
Ironic, 'cause of the queue
Totally broken in you
This means because of the set Q having metrizable space disconnected within it, so space is also disconnected within R since Q is the subset of it.
