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Subject No End in Sight: Debating the Existence of Infinity
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Original Message Despite being in existence for more than 2,000 years, the concept of infinity has endured as an enigmatic, and oftentimes challenging, idea for mathematicians, physicists and philosophers. Does infinity really exist, or is it just part of the fabric of our imaginations?

A panel of scientists and mathematicians gathered to discuss some of the profound questions and controversies surrounding the concept of infinity here Friday (May 31), as part of the World Science Festival, an annual celebration and exploration of science.

Part of the difficulty in trying to solve some of the abstract questions related to infinity is that these problems fall beyond the more established mathematical theories, said William Hugh Woodin, a mathematician at the University of California, Berkeley. [Watch: World Science Festival Highlights]

"It's kind of like mathematics lives on a stable island — we've built them a solid foundation," Woodin said. "Then, there's the wild land out there. That's infinity."

Where it all began

A philosopher named Zeno of Elea, who lived from 490 B.C. to 430 B.C, is credited with introducing the idea of infinity.

The concept was studied by ancient philosophers, including Aristotle, who questioned whether infinites could exist in a seemingly finite physical world, said Philip Clayton, dean of the Claremont School of Theology at Claremont Lincoln University in Claremont, Calif.Theologians, including Thomas Aquinas, used the infinite to explain the relationship between humans, God and the natural world.

In the 1870s, a German mathematician named Georg Cantor pioneered work in a field that became known as set theory. According to set theory, integers, which are numbers without a fraction or decimal component (such as 1, 5, -4), make up an infinite set that is countable. On the other hand, real numbers, which include integers, fractions and so-called irrational numbers, such as the square root of 2, are part of an infinite set that is uncountable.

This led Cantor to wonder about different types of infinity.


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