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

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Question 259928: Why is every irrational number a real number but not every real number is am irrational number?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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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%2F2. This number is rational (as opposed to irrational) and it is real. So not all real numbers are irrational.