Is Transfinite Truly Larger Than Infinity?

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SUMMARY

Transfinite numbers are a concept in mathematics that refers to sizes of infinity, specifically distinguishing between countable and uncountable infinities, often represented by alephs. The discussion clarifies that absolute infinity is a theoretical construct that is larger than transfinite numbers, leading to the hierarchy: absolute infinity > transfinite > infinity. Infinity itself is not a singular number but a general term for quantities that are not finite. Understanding these distinctions is crucial for engaging with advanced mathematical concepts.

PREREQUISITES
  • Understanding of basic mathematical concepts, particularly set theory.
  • Familiarity with the definitions of countable and uncountable sets.
  • Knowledge of ordinal and cardinal numbers.
  • Ability to interpret mathematical articles, such as those found on Wikipedia.
NEXT STEPS
  • Research the concept of cardinality in set theory.
  • Explore the differences between countable and uncountable infinities.
  • Learn about the hierarchy of infinities, including aleph-null and larger cardinalities.
  • Study the implications of absolute infinity and its paradoxes in mathematics.
USEFUL FOR

Mathematicians, students of mathematics, and anyone interested in the philosophical implications of infinity and transfinite numbers will benefit from this discussion.

tacsec
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So transfinite is larger than infinity right?
So if there was an infinitely large object, would a transfinite object be larger than the infinitely large object?
 
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Err, did you actually click on the link? Your question is answered right in the first sentence of that article.
 
rumborak said:
Err, did you actually click on the link? Your question is answered right in the first sentence of that article.

It said absolute infinity was bigger than transfinity. What I got from that was absolute infinity > transfinity > infinity.
 
What I get from the Wiki article on the transfinite is that "absolute infinity" is a concept that leads to paradox. It cannot exist.

I had to go digging for the meaning of "transfinity". It is a noun referring to the general concept of the transfinite. It is not a number.

"Infinity" is not a single well defined number. Comparing it for size against something else that is not a number at all is nonsensical.
 
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Transfinite is a term used to describe various sizes of infinity, countable, non-countable, etc., usually described by alephs. Infinity is a more general term about quantities that are not finite.

This discussion should be in the mathematics forum.
 
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mathman said:
This discussion should be in the mathematics forum.

Done. :smile:
 
Okay I did some extra research kind of get it now. So transfinite just refers to the sets of never ending numbers, and Infinity is supposed to contain all transfinite sets. Is that correct?
 

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