Bigger And Smaller Infinities


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Why are there smaller (bigger) infinitesimals and bigger (smaller ...

Why Are There Smaller (bigger) Infinitesimals And Bigger (smaller ...

Read 28 answers by scientists to the question asked by Geng Ouyang on Oct 31, 2016 Why are there smaller (bigger) infinitesimals and bigger (smaller) infinities in our mathematics? So many people say “infinite thing is not a number”, ... [ReadMore..]

Beyond infinity - Curious

Beyond Infinity - Curious

There is more than one ‘infinity’—in fact, there are infinitely-many infinities, each one larger than before! Aug 19, 2016 ... There's no such thing as the smallest fraction bigger than 0, for starters! But by doing a few mental zigzags, it turns out that it is possible ... [ReadMore..]

Small Infinity, Big Infinity | Science News

Small Infinity, Big Infinity | Science News

A mathematician develops a new proof showing that infinity comes in different sizes. Jan 8, 2008 ... Infinity is bigger than any number. But saying just how much bigger is not so simple. In fact, infinity comes in infinitely many different ... [ReadMore..]

The Different Sizes of Infinity

The Different Sizes Of Infinity

A crucial concept in mathematics. Nov 14, 2013 ... This is another infinite set that looks like it should be bigger than the natural numbers — between any two natural numbers, we have infinitely ... [ReadMore..]

Infinities are not made equal. They come in different sizes | by ...

Infinities Are Not Made Equal. They Come In Different Sizes | By ...

They come in different sizes Jan 26, 2020 ... Well, it turns out that infinity is weirder than that: it comes in ... There's no way one set could be in any sense bigger or smaller than ... [ReadMore..]

elementary set theory - How are some infinities larger than other ...

Elementary Set Theory - How Are Some Infinities Larger Than Other ...

Dec 15, 2014 ... ... in a fashion that assigns bigger and smaller sets some notion of ... has a larger cardinality than X. So any set has more subsets than ... [ReadMore..]

Mathematicians Measure Infinities and Find They're Equal | Quanta ...

Mathematicians Measure Infinities And Find They're Equal | Quanta ...

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the… Sep 12, 2017 ... At the time, mathematicians knew that “the real numbers are bigger than the natural numbers, but not how much bigger. Is it the next biggest ... [ReadMore..]

A Deep Math Dive into Why Some Infinities Are Bigger Than Others ...

A Deep Math Dive Into Why Some Infinities Are Bigger Than Others ...

The size of certain infinite sets has been a mystery. Now, it turns out, each one is different than the next, and they can all be ordered by size Aug 16, 2021 ... There is, however, something akin to a smallest infinity: all infinite sets are greater than or equal to the natural numbers. [ReadMore..]

Why some infinities are bigger than others | Aeon Essays

Why Some Infinities Are Bigger Than Others | Aeon Essays

Georg Cantor showed that some infinities are bigger than others. Did he assault mathematical wisdom or corroborate it? Mar 8, 2017 ... Georg Cantor showed that some infinities are bigger than others. ... or the process of dividing an object into smaller and smaller parts, ... [ReadMore..]

greater and smaller infinity? - Mathematics Stack Exchange

Greater And Smaller Infinity? - Mathematics Stack Exchange

Jun 8, 2018 ... When we say that the limit of a sequence is infinity, we mean that for any number you choose, starting some point, all members of the sequence ... [ReadMore..]

Some infinities are bigger than others

Some Infinities Are Bigger Than Others

Philosophers and scientists have wrestled with questions throughout the ages, but for most of that time ‘infinity’ as a concept was not well-defined. Feb 13, 2018 ... It turns out that the set of all points on a continuous line is a bigger infinity than the natural numbers; mathematicians say there is an ... [ReadMore..]