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-   -   what is zero (http://www.physicsforums.com/showthread.php?t=9350)

 hamlet69 Nov21-03 07:24 AM

what is zero

a simple question

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

 HallsofIvy Nov21-03 11:27 AM

"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, &pi;, &radic;(2) and i.

 gimpy Dec10-03 12:04 AM

0 is the mark i will get on my linear exam if i don't study ;)

 suyver Dec10-03 01:51 AM

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):

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

 himanshu121 Dec10-03 08:34 AM

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

 jcsd Dec10-03 11:25 AM

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.

 HallsofIvy Dec10-03 01:02 PM

Only by 19 days! [:D]

 luther_paul Jan13-04 12:18 AM

zero makes mathematics full of identities and definitions....

 kishtik Feb2-04 12:18 PM

Quote:
 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
$$0 \; = \; e^{i\pi}+1$$

 matt grime Feb2-04 12:26 PM

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

Not in mod 2 arithmetic.

 turin Feb2-04 08:34 PM

What is i or &pi; in mod2?

 suyver Feb3-04 01:30 AM

Quote:
 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.

 matt grime Feb3-04 06:30 AM

Quote:
 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.

 NoEffEks Feb3-04 09:41 AM

Some people consider 0 to be an asymtote. Not saying i do. but some do.

 quartodeciman Feb3-04 11:10 AM

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.

 turin Feb3-04 02:12 PM

Quote:
 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.

 matt grime Feb3-04 03:27 PM

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.

 HallsofIvy Feb3-04 06:58 PM

Quote:
 [i]Originally posted by quartodeciman[/b] 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?"
It sounds a lot better in German, doesn't it. But you are right, it's a cool title.

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