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I came across this article in scientific american article with the title "Mathematicians Measure Infinities, and Find They're Equal". I am quite quite baffled by this. Can someone give me some implications that this new finding might have and how it affect might affect the mathematical community ??

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    $\begingroup$ You have to report more detail about which infinities are equal, not just the title. It's been known for a long time that there are different infinities. Whether two particular infinities are the same or different can be an open question - perhaps one such question was settled and this article is reporting that. $\endgroup$ – Ethan Bolker Sep 17 '17 at 14:27
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    $\begingroup$ @EthanBolker quantamagazine.org/… Have a look at it yourself $\endgroup$ – Ayan Shah Sep 17 '17 at 14:29
  • $\begingroup$ @AyanShah Users should not be expected to follow links to understand the question. Please post the related information here instead. $\endgroup$ – Simply Beautiful Art Sep 17 '17 at 15:00
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    $\begingroup$ Thsi is not a duplicate question.. $\endgroup$ – Henno Brandsma Sep 17 '17 at 15:20
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    $\begingroup$ I've cast the last reopen vote. While this question is very similar to the question "Is there a bijection between the reals and the naturals?, they are different questions: the latter asks about a specific interpretation of the result, while this one asks about the impact/content of that result. $\endgroup$ – Noah Schweber Sep 17 '17 at 15:35
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Here's very rough summary of the context of that article:

It's been known for a long time that there are different infinities. Two particular infinities technically known to mathematicians in this research area as $\frak p$ and $\frak t$ were long thought to be (consistently) different, but no one could prove that.

It turns out that they are equal.

The article goes on to say

[Malliaris and Shelah]'s work has ramifications far beyond the specific question of how those two infinities are related. It opens an unexpected link between the sizes of infinite sets and a parallel effort to map the complexity of mathematical theories.

which begins to answer your question about

implications that this new finding might have and how it affect might affect the mathematical community.

I doubt that it will affect most of everyday advanced mathematics much, but may be very significant in particular areas of research.

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  • $\begingroup$ @NoahSchweber Edited thanks. Not my area of expertise; I was trying to express the gist of the idea simply to answer the OP's question. But the details ought to be right. $\endgroup$ – Ethan Bolker Sep 20 '17 at 12:37

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