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Mathematicians Casually Discovered Two New Infinities

The article from Popular Mechanics discusses the concept of cardinal infinities in mathematics, focusing on how mathematicians categorize different sizes of infinity. It explains that while infinity might seem like a singular, boundless concept, there are actually different "sizes" of infinity, known as cardinal numbers. The article delves into Georg Cantor's work, who introduced the idea that some infinities are larger than others. For instance, the infinity of natural numbers (countable infinity) is smaller than the infinity of real numbers (uncountable infinity). This leads to the concept of the Continuum Hypothesis, which posits that there is no set whose size is strictly between that of the integers and the real numbers. Despite its intuitive appeal, this hypothesis remains unprovable within standard set theory, illustrating the profound and sometimes counterintuitive nature of infinity in mathematics.

Read the Full Popular Mechanics Article at:
[ https://www.popularmechanics.com/science/math/a63121596/exacting-cardinal-infinities/ ]

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