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Unit 3

How Big is Infinity?

Infinity Ancient Mathematicians

Throughout the ages, the notion of infinity has been a source of mystery and paradox, a philosophical question to ponder. As a mathematical concept, infinity is at the heart of calculus, the notion of irrational numbers — and even measurement. This unit explores how mathematics attempts to understand infinity, including the creative and intriguing work of Georg Cantor, who initiated the study of infinity as a number, and the role of infinity in standardized measurement.

Unit Goals

Video Transcript

Video

It takes courage to push beyond the boundaries of understanding, to both explore and explain the boundlessness of the infinite. Numbers and counting are real — intrinsic to our everyday life. But acknowledging their existence ties us to the existence of the infinitude.

Textbook

Textbook

Despite its nebulous reality, the concept of infinity has long teased at mathematicians' minds. Around 500 BC it manifested in the form of incommensurable quantities, a concept akin to heresy in the view of many, particularly the followers of Pythagoras.


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