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It means that it is not algebraic... that is, it is not the root of a polynomial expression with rational coefficients.

There are infinitely more transcendental numbers than algebraic numbers, but only a few are of any practical importance... most prominently pi and e, the base of the natural logarithms.

All (real) transcendental numbers are irrational, but not all Irrational Numbers are transcendental. For example, the square root of two is irrational, but it is not transcendental as it is a root of the equation x2 - 2 = 0, a polynomial expression with rational coefficients.

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Q: What does it mean if a number is transcendental?
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