# What is zero

by hamlet69
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 P: 23 a simple question what is zero "0" does it count as a number? any answers
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,689 "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.
 P: 29 0 is the mark i will get on my linear exam if i don't study ;)
 P: 265 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): $$0 \; = \; e^{i\pi}-1$$ Had enough?
 P: 658 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
 Sci Advisor PF Gold P: 2,226 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.
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,689 Only by 19 days!
 P: 16 zero makes mathematics full of identities and definitions....
P: 115
 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?
That should be
$$0 \; = \; e^{i\pi}+1$$
HW Helper
P: 9,396
 Originally posted by suyver Zero is the only solution of the equation $$x = -x$$.

Not in mod 2 arithmetic.
 HW Helper P: 2,327 What is i or π in mod2?
P: 265
 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.
HW Helper
P: 9,396
 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

and n is either 0 or 1 depending on n odd or even resp.
 P: 2 Some people consider 0 to be an asymtote. Not saying i do. but some do.
 P: 383 I like the title of a monograph by nineteenth-century German mathematician Richard Dedekind. "Was sind und was sollen die Zahlen?" This can be rendered roughly in English by the following. What are numbers, and what should they be?" I think that is the fundamental question behind this topic.
HW Helper
P: 2,327
 Originally posted by matt grime ... n is either 0 or 1 depending on n odd or even resp.
Not n, &pi;. That is pi.

I'm still trying to understand that bit about i.
 Sci Advisor HW Helper P: 9,396 do you know what the integers are mod 2? where did pi come from? if that's all too much, then you probably don't want to know about maximal ideals in the ring of integers by n I assumed you mean 1+1+1...+1, n times. The key thing to understand is that when i introduced mod 2 arithmetic, i was pointing out that the question, and many of the answers were assuming that it was posed in the the real numbers. that is notthe only place where zero occurs.
Math
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