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Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...
Rational numbers (): Numbers that can be expressed as a ratio of an integer to a non-zero integer. [3] All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers (): Numbers that correspond to points along a line. They can be positive, negative, or zero.
The n th roots of the denominators of the n th convergents are close to Khinchin's constant, suggesting that is irrational. If true, this will prove the twin prime conjecture. [113] Square root of 2: 1.41421 35624
1.3 Every rational number is either a terminating or repeating decimal. ... Examples of such irrational numbers are ... 0.0 5: 1 1 / 19 0. ...
A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Negative denominators are allowed, but are commonly avoided, as every rational number is equal to a fraction with positive denominator.
The real numbers include the rational numbers, such as the integer −5 and the fraction 4 / 3. The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) are the root of a polynomial with integer coefficients, such as the square root √2 = 1.414...; these are called algebraic numbers.
0.0 5 = 5/90 0.000 392 = 392/999000 ... , the algebraic fraction is called a rational fraction (or rational expression). An irrational fraction is one that is not ...
For bases r and s with log r / log s rational (so that r = b m and s = b n) every number normal in base r is normal in base s. For bases r and s with log r / log s irrational, there are uncountably many numbers normal in each base but not the other. [10] A disjunctive sequence is a sequence in which every finite string appears. A normal ...