what is zero


by hamlet69
Tags: None
hamlet69
hamlet69 is offline
#1
Nov21-03, 07:24 AM
P: 23
a simple question

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

any answers
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
HallsofIvy
HallsofIvy is offline
#2
Nov21-03, 11:27 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882
"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.
gimpy
gimpy is offline
#3
Dec10-03, 12:04 AM
gimpy's Avatar
P: 29
0 is the mark i will get on my linear exam if i don't study ;)

suyver
suyver is offline
#4
Dec10-03, 01:51 AM
suyver's Avatar
P: 265

what is zero


Zero is the only solution of the equation [tex] x = -x[/tex].

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):

[tex] 0 \; = \; e^{i\pi}-1[/tex]

Had enough? [:D]
himanshu121
himanshu121 is offline
#5
Dec10-03, 08:34 AM
himanshu121's Avatar
P: 661
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
jcsd is offline
#6
Dec10-03, 11:25 AM
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.
HallsofIvy
HallsofIvy is offline
#7
Dec10-03, 01:02 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882
Only by 19 days! [:D]
luther_paul
luther_paul is offline
#8
Jan13-04, 12:18 AM
P: 16
zero makes mathematics full of identities and definitions....
kishtik
kishtik is offline
#9
Feb2-04, 12:18 PM
P: 115
Originally posted by suyver
Zero is the only solution of the equation [tex] x = -x[/tex].

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):

[tex] 0 \; = \; e^{i\pi}-1[/tex]

Had enough? [:D]
That should be
[tex] 0 \; = \; e^{i\pi}+1[/tex]
matt grime
matt grime is offline
#10
Feb2-04, 12:26 PM
Sci Advisor
HW Helper
P: 9,398
Originally posted by suyver
Zero is the only solution of the equation [tex] x = -x[/tex].

[:D]

Not in mod 2 arithmetic.
turin
turin is offline
#11
Feb2-04, 08:34 PM
HW Helper
turin's Avatar
P: 2,327
What is i or π in mod2?
suyver
suyver is offline
#12
Feb3-04, 01:30 AM
suyver's Avatar
P: 265
Originally posted by kishtik
That should be
[tex] 0 \; = \; e^{i\pi}+1[/tex]
I hang my head in deep shame. [*(] You are (of course) very right.
matt grime
matt grime is offline
#13
Feb3-04, 06:30 AM
Sci Advisor
HW Helper
P: 9,398
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

so the answer is i=1

and n is either 0 or 1 depending on n odd or even resp.
NoEffEks
NoEffEks is offline
#14
Feb3-04, 09:41 AM
P: 2
Some people consider 0 to be an asymtote. Not saying i do. but some do.
quartodeciman
quartodeciman is offline
#15
Feb3-04, 11:10 AM
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.
turin
turin is offline
#16
Feb3-04, 02:12 PM
HW Helper
turin's Avatar
P: 2,327
Originally posted by matt grime
... n is either 0 or 1 depending on n odd or even resp.
Not n, π. That is pi.

I'm still trying to understand that bit about i.
matt grime
matt grime is offline
#17
Feb3-04, 03:27 PM
Sci Advisor
HW Helper
P: 9,398
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
HallsofIvy is offline
#18
Feb3-04, 06:58 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882
[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.


Register to reply