Real Numbers
The real numbersRare "all the numbers" on thenumber line. They include therationalsandirrationalstogether.
Even though real numbers are basic to all mathematics, to give a correct definition of the real numbers is a little bit advanced. If you've studied limits, the real numbers are the set of all possible limits of convergent sequences of rational numbers. If you haven't, don't worry about it yet; just think of them as the rationals plus the irrationals.
There areinfinitely manyreal numbers, just as there are infinitely manyrationalornatural numbers, but it can be proved that the infinity of the real numbers is, in some way, abiggerinfinity!
There are even "bigger" infinities, but you should take a set theory class for that!
TheVenn diagrambelow shows the relationships of the various sets of numbers.
