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    • What Is Infinity? Infinity Facts and Examples
      • Mathematicians deal with different sizes of infinity. The sets of positive whole numbers (numbers greater than 0) and negative whole numbers (numbers less than 0) are infinite sets of the same size. But, if you combine the two sets you get a new infinite set that is twice as large. You can add a number to infinity to make it larger.
      sciencenotes.org/what-is-infinity-infinity-facts-and-examples/

      What Is Infinity? Infinity Facts and Examples

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  3. www.scientificamerican.com › articleMathematicians Measure Infinities, and Find They're Equal

    Sep 16, 2017 · In a breakthrough that disproves decades of conventional wisdom, two mathematicians have shown that two different variants of infinity are actually the same size.

  4. blog.russelldmatt.com › 2020/01/21 › different-infinitiesDifferent infinities, and why it matters | Blog

    Jan 21, 2020 · What does that even mean? Here is a rigorous definition of what it means for two sets (infinite or not) to be the same size: Two sets are the same size if there is an invertible function that maps between them. With that in mind, let’s work through our grade-school examples.

  5. math.stackexchange.com › questions › 258664What does the notion of different sizes of infinity really mean?

    Mathematicians agree that this means that it is possible to find a bijection $$ A\longleftrightarrow B. $$ Thus, the existence of infinities of various sizes means that it is possible to find $A$ and $B$ both infinite which do not admit a bijection as above.

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  7. sciencenotes.org › what-is-infinity-infinity-factsWhat Is Infinity? Infinity Facts and Examples

    Jun 16, 2021 · Mathematicians deal with different sizes of infinity. The sets of positive whole numbers (numbers greater than 0) and negative whole numbers (numbers less than 0) are infinite sets of the same size. But, if you combine the two sets you get a new infinite set that is twice as large.

  8. en.wikipedia.org › wiki › InfinityInfinity - Wikipedia

    The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets. Among the axioms of Zermelo–Fraenkel set theory, on which most of modern mathematics can be developed, is the axiom of infinity, which guarantees the existence of infinite sets. [1] .

  9. www.quantamagazine.org › how-can-some-infinitiesHow Can Some Infinities Be Bigger Than Others? - Quanta Magazine

    Apr 19, 2023 · In this episode, Steven Strogatz chats with his fellow mathematician Justin Moore of Cornell University about how one infinity can be bigger than another (and whether we can be sure that there isn’t an intermediate infinity between them).

  10. www.scientificamerican.com › article › strange-butStrange but True: Infinity Comes in Different Sizes

    Jul 19, 2007 · As German mathematician Georg Cantor demonstrated in the late 19th century, there exists a variety of infinities—and some are simply larger than others. Take, for instance, the so-called...