The standard view of continuums,like the real number line, 
is that they are composed solely of numbers stacked upon numbers.
But if you take all of the rational numbers and stack them upon each other
you’ll find that that entire stack will have zero measure, in other words, zero thickness. 
But the real number line does have thickness.
So what we say is that in between any two different real numbers lie uncountably infinite numbers.
And so you might say that it is this uncountability which gives the real number line its thickness. 
Let’s assume that this deck might have some duplicate cards, and that the cards are in order from least to greatest.
We’ll cut the deck to select a random number, a King, which represents a ten. 
This number can be thought to divide the number line into two partitions:
the numbers less than or equal to it and the numbers greater than or equal to it.
But what is the least number greater than it?
Well, there is no least number greater than it.
And what is the greatest number less than it?
There is no greatest number less than it.
But we said that this deck is composed solely of numbers, so these cards are numbers.
But perhaps they are not greater than 10, nor less than 10, but instead they are equal to 10.
These three cards are duplicates, and they represent a singular number.
And IF we are allowed to take this reasoning to it’s limit,
IF every card is equal to its neighbours,
does that mean that the real number line is composed of a singular number?
Or was a mistake made along the way?
Maybe continua are not composed solely of numbers.
