pi and e are Irrational Numbers. Without them most of geometry, trigonometry, calculus or probability distributions would not be defined.
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Two of the most important numbers in advanced mathematics are pi and e and both are irrational.
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.
How an irrational number is estimated depends on the nature of the number. The reason for estimating them is that two of the most important numbers in mathematics: pi in geometry and e in calculus, are both irrational. Also, the diagonal of a unit square is of length sqrt(2), an irrational. Irrational numbers crop up everywhere: there are more irrational numbers than there are rational.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
All irrational numbers are not rational.