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irrational∗
yark†
2013-03-21 12:43:42
An irrational number is a real number which cannot be represented as a
ratio of two integers. That is, if x is irrational, then
x 6=
a
b
with a, b ∈ Z and b 6= 0.
Examples
√
1. p 2 is irrational for p = 2, 3, . . .,
√
2. π, e, and p 2 for p = 2, 3, . . ., are irrational,
3. It is not known whether Euler’s constant is rational or irrational.
Properties
1. It a is a real number and an is irrational for some n = 2, 3, . . ., then a is
irrational (proof).
2. The sum, difference, product, and quotient (when defined) of two numbers,
one rational and another irrational, is irrational. (proof).
∗ hIrrationali
created: h2013-03-21i by: hyarki version: h30661i Privacy setting: h1i
hDefinitioni h11J82i h11J72i
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