is zero $\huge 0$ a positive multiple of every integer ?

Question

is zero   $\huge 0$    a positive multiple of every integer ?

kainui · Answer

If by positive you mean not less than 0 and by multiple you mean a*n is a multiple of n, then yes.

mathmath333 · Answer

so it is positive multiple of every integer .?

mathmath333 · Answer

i m very confused

kainui · Answer

It depends on what you define positive to mean. Does positive mean greater than 0 or greater than and equal to zero? Unless your class has a specific definition of positive, this is just a vague question.

mathmath333 · Answer

i dont know what exactly positive means $0>$ or $0\geq $ , i want an undisputed  universally accepted fact.

ganeshie8 · Answer

0 is not positive, not negative

mathmath333 · Answer

so that implies its neither a positive multiple ?

ganeshie8 · Answer

nonnegative integers include 0,1,2,3,...
nonpositive integers include 0,-1,-2,-3,...

ganeshie8 · Answer

for quick checks, we can rely on wolfram, it has pretty consistent definitions for most number theory terms http://mathworld.wolfram.com/NonpositiveInteger.html

mathmath333 · Answer

if the question asks what are the first 5 multiples of 5 ?
and 
 what are the first 5 positive multiples of 5 ?
what should i write

ganeshie8 · Answer

5, 10, 15, 25, 30 are the first five positive multiples of 5

ganeshie8 · Answer

*missed 20

mathmath333 · Answer

and ehat about this
$\text{what are the first 5} \cancel {positive } \text{multiples of 5 ?}$

ganeshie8 · Answer

the question just wants you list the familiar multiplication table :
$$5\times 1 = 5\5\times2=10\5\times 3 = 15\5\times 4=20\5\times 5=25$$

mathmath333 · Answer

so if for the question 
$\text{what are the first 5 multiples of 5}$
i should not include $0$

ganeshie8 · Answer

$$5\times 0 = 0$$

Oh you mean you want to include that ?

mathmath333 · Answer

yes that one!

ganeshie8 · Answer

yeah you may include that but just keep in mind 0 is not positive

mathmath333 · Answer

ohk thnks so 
first five multiples of 5
are 0 ,5 ,10, 15, 20

kainui · Answer

Yeah I guess I was thinking for some reason of how there's the confusion between is 0 a natural number or not, which is a slightly different question.

ganeshie8 · Answer

i would stick to 5,10,15,20,25

mathmath333 · Answer

but this page and also says that 0 is a multiple of everything http://en.wikipedia.org/wiki/Multiple_%28mathematics%29 http://www.manhattanprep.com/gmat/forums/number-properties-is-0-a-multiple-of-every-integer-t4998.html

ganeshie8 · Answer

thats right because 
$$0 = x\times 0 $$

for any integer $x$

mathmath333 · Answer

in many books, i found that they dont include 0

kainui · Answer

Yeah there are two parts going on here. You are looking for positive multiples, but if you want to look at strictly multiples of 5, this is your infinite list: $$\Large ... ,-25, -5, 0, 5, 25, ...$$

mathmath333 · Answer

ok so postive multiple $\cancel 0$
 and only for only multiple $0~~\checkmark$ 

i should stick to this

ganeshie8 · Answer

i guess question should clarify what it is talking about. Knowing 0 is neither positive nor negative is sufficient and rest should become clear based on context of the quesiton..