Mathematicians Casually Discovered Two New Infinities

Science and Technology Science and Technology

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[ Wed, Dec 11th 2024 ] - Popular Mechanics

Mathematicians Casually Discovered Two New Infinities

^{Published on 2024-12-11 12:02:45 - Popular Mechanics}

Mathematicians have long known that there are many kinds of infinities (technically, there are an infinity of them). Mathematicians revealed two new kinds of infinity
called exacting and ultra-exacting
infinities that appear to contradict foundational mathematics.

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/ ]

N@N

Mathematicians Casually Discovered Two New Infinities