Real Numbers Quotes

God made integers, all else is the work of man.

There are infinite numbers between 0 and 1.

The story of pi has been extensively told, no doubt because its history goes back to ancient times, but also because much of it can be grasped without a knowledge of advanced mathematics.

Nature never uses prime numbers. But mathematicians do.

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

Square root of a cosine? How is that ever going to be useful?

I think we did a great job of putting together a program that would have made good e-books available had people been buying e-books in any real numbers.

Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.

Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.

The infinite in mathematics is alway unruly unless it is properly treated.

The seventeenth century witnessed the birth of modern science as we know it today. This science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science-a dependence on numbers, on real numbers of actual experience.

The fun little proofs that you can do with algebra - they are sort of like crowd pleasers in a way. Like, the .9 repeating equaling one. It doesn't take a lot of algebra to prove that, and it's really fun. It kind of wows people. It's like they're watching magic happen right before their eyes.