SOLUTION: Why is every irrational number a real number but not every real number is am irrational number?

Question 259928: Why is every irrational number a real number but not every real number is am irrational number?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 . This number is rational (as opposed to irrational) and it is real. So not all real numbers are irrational.
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