Sentence examples for use of irrational numbers from inspiring English sources

However, without the use of irrational numbers, there is no way to specify with cardinal numbers exactly how much longer the diagonal is than the side of a square.

The employment of irrational numbers greatly increases the scope and usefulness of arithmetic.

His uses of "irrational number," "incommensurable," "truth-functional" and many other smart-sounding terms betray at best an indifference to what they actually mean.

Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form.

A frequently cited factor is the discovery of irrational numbers.

Week 5: Dedekind's theory of irrational numbers.

Or poems enacting the formation and breakdown of community as expositions of irrational numbers?

These experiences led Dedekind to see the need for a redefinition of irrational numbers in terms of arithmetic properties.

Cantor has shown that we can construct "infinitely many" diverse systems of irrational numbers, but we cannot construct an exhaustive system of all the irrational numbers (RFM II, §29).

One lesson to be learned from this, according to Wittgenstein (RFM II, §33), is that "there are diverse systems of irrational points to be found in the number line," each of which can be given by a recursive rule, but "no system of irrational numbers," and "also no super-system, no 'set of irrational numbers' of higher-order infinity".

From Cantor's proof, however, set theorists erroneously conclude that "the set of irrational numbers" is greater in multiplicity than any enumeration of irrationals (or the set of rationals), when the only conclusion to draw is that there is no such thing as the set of all the irrational numbers.