Is Transfinite Truly Larger Than Infinity?

[tacsec]

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?

 

[jbriggs444]

Transfinite means larger than finite. One transfinite quantity might or might not be larger than another.

http://en.wikipedia.org/wiki/Transfinite_number

 

[tacsec]

Transfinite means larger than finite. One transfinite quantity might or might not be larger than another.

http://en.wikipedia.org/wiki/Transfinite_number

So is transfinity bigger than infinity?

 

[rumborak]

Err, did you actually click on the link? Your question is answered right in the first sentence of that article.

 

[tacsec]

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.

 

[jbriggs444]

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.

 

[mathman]

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.

 

[berkeman]

This discussion should be in the mathematics forum.

Done.

 

[tacsec]

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?

 

[mathman]

http://en.wikipedia.org/wiki/Transfinite_number

I hope the above helps. Transfinite is used for a specific type of discussion (ordinal numbers, cardinal numbers), while infinite is a general term.