## what is zero

a simple question

what is zero "0" does it count as a number?

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 Recognitions: Gold Member Science Advisor Staff Emeritus "0" is the cardinality of the empty set (that's one definition). "0" is the additive identity (that's another). Yes, 0 is a number just like -1, π, √(2) and i.
 0 is the mark i will get on my linear exam if i don't study ;)

## what is zero

Zero is the only solution of the equation $$x = -x$$.

Also, zero is both the limit of the largest negative numbers and the limit of the smallest positive numbers...

Naturally, even more important (due to Euler):

$$0 \; = \; e^{i\pi}-1$$

 0 was transferred from India to Arabians and to world I dont know much of its importance given by Our Ancient Seers But mathematically it is an essence in every field Metaphysically it represents DEATH,GLOOMY,INAUSPICIOUS
 Recognitions: Gold Member Science Advisor Zero is the identity element in addition (of vectors, integers, etc.) edited to add: looks like HallsofIvy has beaten me to the punch on that defintion.
 Recognitions: Gold Member Science Advisor Staff Emeritus Only by 19 days! [:D]
 zero makes mathematics full of identities and definitions....

 Originally posted by suyver Zero is the only solution of the equation $$x = -x$$. Also, zero is both the limit of the largest negative numbers and the limit of the smallest positive numbers... Naturally, even more important (due to Euler): $$0 \; = \; e^{i\pi}-1$$ Had enough? [:D]
That should be
$$0 \; = \; e^{i\pi}+1$$

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 Originally posted by suyver Zero is the only solution of the equation $$x = -x$$. [:D]

Not in mod 2 arithmetic.
 Recognitions: Homework Help What is i or π in mod2?

 Originally posted by kishtik That should be $$0 \; = \; e^{i\pi}+1$$
I hang my head in deep shame. [*(] You are (of course) very right.

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 Originally posted by turin What is i or π in mod2?

i is defined to be the square root of -1 isn't it? well, then -1=1 (mod 2) and the polynomial

x^2-1 = (x+1)(x+1) mod 2