0 a number that cannot be expressed as the ratio of two whole numbers
1 a number that cannot be expressed as the ratio (= comparison of two numbers by division) of two whole numbers
Every infinite continued fraction converges to an irrational number.
Conversely, every irrational number is decomposable, in one and only one way, into a continued fraction which is necessarily infinite.
Recall that each number has at most two binary expansions and any irrational number has exactly one.
Thus, for example, an irrational number is the limit of different fractions which have values approaching it more and more.
Incidentally, this "irrational flow on a torus," where 1 /2 is an irrational number, determines one of the simpler examples of chaotic behavior.
Let x be an irrational number.
By taking quantitative values (numbers) out of the equation, he avoided the trap of having to express an irrational number as a number.
An irrational number has an infinite non-repeating representation in all integer bases.
