is-a-real-number-

Question Number 205577 by BaliramKumar last updated on 25/Mar/24

is \infty a real number ?

Commented by mr W last updated on 25/Mar/24

i t i s o n l y a s y m b o l . i t m a y h a v e

d i f f e r e n t m e a n i n g s d e p e n d i n g o n

i n w h i c h c o n t e x t i t i s u s e d .

g e n e r a l l y p e o p l e u s e i t t o

d e s c r i b e s o m e t h i n g w i t h o u t a n y

l i m i t (b o u n d a r y) .

Commented by BaliramKumar last updated on 25/Mar/24

Commented by mr W last updated on 25/Mar/24

h e r e a c o n t e x t i s g i v e n, t h e t o p i c i s

a b o u t n u m b e r s . w h e n t a l k i n g a b o u t

n u m b e r s, \infty r e f e r s t o

- \infty < x < + \infty

b u t s t i l l w e c a n n o t s a y \infty i s a n u m b e r

o r \infty i s a r e a l n u m b e r .

Commented by BaliramKumar last updated on 25/Mar/24

i think Q is wrong

e is also irrational

Commented by mr W last updated on 25/Mar/24

y e s, q u e s t i o n i s n o t a g o o d o n e . t h e

a n s w e r g i v e n i s a l s o w r o n g .

Answered by TheHoneyCat last updated on 31/Mar/24

In standard math ({Russel}^{'} s set theory,

{Bourbaki}^{'} s construction \dots ect \dots)

R (the set of real numbers) is defined as the

completion of Q (i . e . the limits of

bounded increasing sequences in Q) .

So in all the usual meanings of “ \infty^{″}

\infty \notin R

This includes : formal topological closure of R

\bar{R} = R ⨄ {+ \infty, - \infty}

The projective plane {RP}^{1} where \infty := [0 : 1]

The sur - real extension \infty = ℵ_{0} (or any

“ {infinite}^{″} number)

But of course, there are numerous areas of

math where this is not explicitely stated

and we {don}^{'} t pay attention wether R refers

to real numbers or some extentions \dots