Symbol for Finite: Exploring the Use and Interpretation of ##<\infty##

[LightningInAJar]

TL;DR Summary

Is there a symbol for finite?

I know there's a symbol for infinite. But is there a finite one?

 

[fresh_42]

It is usually written $<\infty$ or if it was done better $=C<\infty$.

 

[Nugatory]

How about just specifying that the number in question is an element of the reals? There are no infinite reals.

 

[LightningInAJar]

It is usually written $<\infty$ or if it was done better $=C<\infty$.

Dumb question. What is C in this case?

 

[fresh_42]

Some constant (finite) number. The real number @Nugatory spoke of.

 

[7777777]

How about just specifying that the number in question is an element of the reals? There are no infinite reals.

Is infinity undefined in reals ?

 

[Mark44]

Finite and infinite are both adjectives. Although there is a noun form for infinity, I'm not aware of the existence of "finity" as a word in English. If so, we have a symbol for and a word for infinity, $\infty$, we have neither a word or symbol for its opposite.

 

[DaveE]

Finite and infinite are both adjectives. Although there is a noun form for infinity, I'm not aware of the existence of "finity" as a word in English. If so, we have a symbol for and a word for infinity, $\infty$, we have neither a word or symbol for its opposite.

I prefer to think of them as mathematical constructs. English isn't necessary, which is good if you don't speak it.

 

[fresh_42]

Is infinity undefined in reals ?

Yes. In some cases the set $\overline{\mathbb{R}}=\mathbb{R}\cup \{\pm \infty \}$ is used. It is referred to as extended real numbers.

 

[Frabjous]

logically
finite = not infinite $\Rightarrow \neg\infty$ or $!\infty$ or $\infty’$ or $\overline{\infty}$


This page references the OED and says that finity is a word.
https://en.wiktionary.org/wiki/finity

 

[fresh_42]

logically
finite = not infinite = ¬∞ or !∞ or $\infty$’ or $\overline{\infty}$

I'm sure mathematicians prefer $< \infty$ over those code style notations.

This page references the OED and says that finity is a word.
https://en.wiktionary.org/wiki/finity

A slightly better reference:
https://www.etymonline.com/search?q=finity

 

[Frabjous]

I'm sure mathematicians prefer <∞ over those code style notations.

Given the mathematical disdain for logic symbols, may we postulate a dearth of Vulcan mathematicians?

A slightly better reference:
https://www.etymonline.com/search?q=finity

I liked the quotes in mine

1. • 1874, Hawthorne, Julian, chapter 31, in Idolatry: A Romance:
     He was calm in the conviction that he could measure and calculate the universe […] He matched finity against the Infinite.
   • 1899, London, Jack, The White Silence:
     Nature has many tricks wherewith she convinces man of his finity.
   • 1987, Fraser, Julius Thomas, Time, the Familiar Stranger, →ISBN, page 37:
     In a very non-Aristotelian fashion, Nicholas of Cusa produced a synthesis of finity and infinity.
   • 2006, Witzsche, Rolf A. F., Universal Divine Science: Spiritual Pedagogicals, →ISBN, page 106:
     We […] labor to find our identity in the infinite in spite of our encumberment in finity.
2. • 1734, Watts, Isaac, “A Brief Scheme of Ontology”, in Philosophical Essays on Various Subjects, 6th edition, London: T. Longman, T. Fields and C. Dilly, published 1794, page 370:
     Disagreement in substance or essence […] may be called Disproportion, as there is a disproportion between finities and infinities, i.e. there is no proportion between them.
   • 1837 September 2, “The Transcendalist's Dialogues: No. IX”, in The Shepherd, volume 3, number 10, page 79:
     If we imagined a person capable of comprehending infinity, we should merely think that he was able infinitely to add up finities.
   • 1884 January 1, “Prayer and Science”, in Methodist Quarterly Review (4th)‎[1], volume 66, page 8:
     And this condescension of infinite Perfection to the finities—to their imperfections, contingencies, and littlenesses—is the very result of its perfection.

 

[MidgetDwarf]

It is usually written $<\infty$ or if it was done better $=C<\infty$.

I think one has to be careful using that symbol. I have seen it mean convergence.