transfinite
1
9.9
- noun
- /trænsˈfaɪnɪt/
- Specialized
- For instance, mathematicians do not need real-world experiences proving the existence of transfinites to make use of transfinite numbers in some demonstrations.
Examples
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Still not sure that "the final digit of pi" is in any way a sensible statement, but the concept of transfinites is about the point in higher math where my head starts to melt.
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I know it handles the transfinite ordinals just fine.
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George Cantor was the originator of set theory and of the study of transfinite numbers.
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They're great at doing transfinites and infinitesimals. But 1/0 is fundamentally meaningless.
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The closest the surreals come is the relation between transfinites and infinitesimals: the first non-finite surreal is ?; 1/? = ?.
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Also, see this interesting stuff from the blog "A Neighborhood of Infinity" about how an "infinity" (specifically a transfinite ordinal) can describe a 1 Player Game that anyone can play and which is guaranteed to terminate after a finite number of moves.
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George Cantor developed theories that revolutionized our understanding of transfinite numbers in mathematics.
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In set theory, transfinite numbers help mathematicians explore concepts beyond finite limits.
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Mathematically, transfinite sizes exceed any finite quantity, posing unique challenges in calculations.
Surface Forms
Morphology
Etymology
The noun transfinite also comes from trans- 'beyond' and finite 'has an end', and it names the group of numbers or sizes that go beyond every finite number. A mathematician named Cantor used this idea to show that there can be different sizes of infinity, which is why the transfinite refers to those very large, non-finite sizes.