What is a mole?

Here is the text book definition of the mole.
Mole – The amount of substance that contains as many elementary entities (atoms, molecules, or other particles) as there are atoms in exactly 12 grams of the carbon-12 isotope.

Now what does that mean exactly?  It means that a mole is just a number.  Just as a pair is equal to 2, a trio is equal to 3, and a dozen is equal to 12. 

One mole is equal to 602200000000000000000000 or 6.022x10²³.  Where did the number 6.022x10²³ or 602200000000000000000000 come from?  Well, there happens to be 602200000000000000000000 atoms in exactly 12 grams of the carbon-12 isotope

Examples:
a) If one dozen = 12
Then two dozen = 2(12) = 24

b) If one mole = 6.022x10²³
Then two moles = 2(6.022x10²³)

c) If one pair = 2
Then two and a half pair = 2.5(2) = 5

d) If one mole = 602200000000000000000000
Then two and a half moles = 2.5(6.022x10²³)