is-zero-a-natural-number-0-N-

Question Number 114807 by Eric002 last updated on 21/Sep/20

i s z e r o a n a t u r a l n u m b e r 0 \in N ?

Commented by MJS_new last updated on 21/Sep/20

there seem to be two different definitions

of N, both are in use \dots confusion \dots

old definition N = {1, 2, 3, \dots}; N \cup {0} = N_{0}

new definition N = {0, 1, 2, \dots}; N ∖ {0} = N^{★}

so the answer depends on in which country

and on which school you are

when I was in school (a zillion years ago) we

leaned these things one after the other :

(1) N : a s y o u c o u n t (nobody would start to

count by 0) .

(1.1) addition is always possible in N

(1.2) multiplication is always possible in N

but n \times 1 = n

(1.3) substraction only as a test of addition

a + b = c \Rightarrow c - b = a \land c - a = b

(1.4) substraction a - b possible only if a > b ?

\Rightarrow

(2) Z = N \cup {\dots - 2, - 1, 0} these are magical

numbers we need to substract without limits

a - b = x always solveable in Z

(2.1) 0 n e u t r a l e l e m e n t o f a d d i t i o n

(2.2) 1 n e u t r a l e l e m e n t o f m u l t i p l i c a t i o n

then Q (a \div b = x solveable), then R (all non -

periodic numbers like \sqrt{2}, π; later e \dots),

finally C

Commented by Eric002 last updated on 21/Sep/20

t h a n k y o u f o r e x p l a n i n g b u t w h a t i s t h e

d i f f e r e n c e b e t w e e n N a n d N^{*}

Commented by MJS_new last updated on 21/Sep/20

the old N is the same as the new N^{★}

= {1, 2, 3, \dots}

the old N_{0} is the same as the new N

= {0, 1, 2, \dots}

Commented by Eric002 last updated on 21/Sep/20

t h a n k y o u s i r

Commented by Rasheed.Sindhi last updated on 21/Sep/20

W h y {i s n}^{'} t t h e r e a n y i n t e r n a t i o n a l

i n s t i t u t e w h i c h p l a y r o l l i n t h i s

c o n n e c t i o n ? W h i c h m a k e

s t a n d a r d s s o t h a t s u c h

c o n f u s i o n s b e k i l l e d ?

Commented by MJS_new last updated on 21/Sep/20

standards are no longer accepted in the age

of internet; {everybody}^{'} s own opinion counts

more than any standard

Commented by Rasheed.Sindhi last updated on 21/Sep/20

T h a n k S s S i r!