Question 259928
The set of irrational numbers are real since they can be represented as decimal numbers. The decimal patterns don't repeat (or don't have a clear pattern), but they are still real numbers. So if you have an irrational number, it is also a real number.



On the other hand, if you have a real number, you aren't guaranteed it's irrational. Take for example the number {{{1/2}}}. This number is rational (as opposed to irrational) and it is real. So not all real numbers are irrational.