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Hello, Jonathan Swift encapsulated the counterintuitive character of infinity with

unsousion's style.

So, naturalist observe, a flea, he wrote, has smaller fleas on him that prey, and these have smaller fleas to bite

them, and so proceed, ad infinitum.

Alas, the developing utility which mathematicians put to the idea of infinity didn't find the English philosopher

Thomas Hobbs quite so relaxed.

When confronted with a diagram depicting an infinite solid, whose volume was finite, he wrote,

to understand this for sense, it is not required

that a man should be a geometrician or logician,

but he should be mad.

Yet philosophers and mathematicians have continued to grapple with the unending and it's a core concept in modern maths.

So what is mathematical infinity?

Are some infinities bigger than others and does infinity exist in nature.

With me to discuss the mathematics of the infinite is Ian Stewart, Professor of Mathematics at the

University of Warwick, Sarah Reese, reader in pure mathematics at the University of Newcastle, and Robert Kaplan, co-founder and

co-director of the Math Circle at Harvard University, and author of a new book, The Art of the Infinite,

our Lost Language of Numbers. Ian Stewart, let's start this with Zeno. the infinite

and the infinite,

and one of his language, the infinitesimal, and one of his paradox,

the best known is the tortoise in the hair, the race between them and how

...