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They define irrational numbers
The numbers 8 and 23 are irrational number because they do not go into any more number than themselves. This is taught in math.
Mathamatical pi is an irrational number. It classifys as an irrational number because the numbers never repeat and pi is a never ending number.
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
I don't understand what you mean by deeper, but the cardinality of irrational numbers, Aleph-One, is greater than the cardinality of rationals, Aleph-Null. That is to say, there are more irrational numbers than rationals. [If you treat infinity as a number, there are infinity to the power of infinity irrational numbers compared with "just infinity" for rationals.]