What exactly is zero?

Question

I am aware that when we use a numerical measuring system we encounter "negative numbers" as in the temperature system and that in celcius, zero is designated the freezing point of water, and in the kelvin, absolute zero is total absence of thermal energy so even atoms do not vibrate.
In maths, even numbers like 10E-34 are above zero as you cant have a negative amount of something tangeable.
So what exactly is zero - how does it fit in maths? Is it a symbol or is it a something even tho its a nothing?

ok there is slight kinetic motion of particles at absolute zero, but this is due to the Heidenberg uncertainty principle which states that if one knows the speed of a particle u cant know its position and vice versa. Brownian motion is the movement of molecules in air.

wow - you have helped enormously - thats why i love answers. I could get this out of wiki, but it might not make sense. With so many fine minds with a bit of time to spare, I get the thoughts of many and by the looks of it a few are connecting with my badly put together question - thankx

Answer 1

Apparently many out there are suffering from what my college professor called "number/numeral disease." Zero (like all numbers) has a dual identity as a concept indicating value and as a symbol representing that concept.
The number zero or the concept of zero tells you how many of something you have. If you have 3 apples, the number 3 is a property of the set and doesn't change based on who is counting. If you don't have any apples, the number of apples you have may be obvious to you, but you need a symbol to communicate that to someone else.
The numeral zero is what we use in mathematics or even in English to communicate that we have counted something and came up with nothing. It simply represents the concept of zeroness. These symbols or numerals are interchangeable: nada, zero, zip, zilch, 0, Ø, cero, or nothing.

so zero is a symbol and it is a concept: a something that reminds you that you only have nothing.



For those of you who noted the usefulness of zeros in representing other numbers, the number 10 can easily be expressed without the numeral 0 by using base 3:
31 (base three) = 10 (base 10)
Since we count by 10's, the numeral zero appears much more often in our representations of numbers

In physics, the understanding of what goes on at absolute zero doesn't have anything to do with the number or the symbol 0.
Note that absolute zero is -459 degrees Fahrenheit or -273 Celsius. The zero is just an arbritray choice.

...and Brownian motion is random motion in any fluid, such as a nice hot cup of tea.

Answer 2

From an abstract standpoint zero is the number e that as the following properties:
a+e=a
a*e=e
for all a

0 is just the zero for the number system that we are most familiar with.


In the field of abstract algebra there are constructs called rings, fields, and groups* that are basically number systems that follow certain rules. In these constructs addition and multiplication can be very different than what you are used to.
Heres an example consider a system with just two numbers 1&2
Let 1+1 =2, 2+1= 1
Also let 1*1 =1, 2*1=2, 2*2=2

Notice that in this system 2+a=a and 2*a=2 for all a
Thus 2 is the zero of the system

*groups only contain the multiplication operation
so the zero of a group is simply the element e s.t.
a*e=e for all a

Answer 3

Zero is a very specific concept and once did not exist. The idea of a zero comes from India, the idea spread through the Arab world to Europe. At first the idea of using a zero in maths was considered a heresy by the Catholic Church (which is why there is no zero in Roman numerals) but later became acceptable when it was realised that by using a zero in mathamatics more money could be made in financial transactions.
So in some ways in western society zero is a quite recent addition to the standard numbers and thus does not 100% fit in with how numbers are integrated into thought as a whole. In India and other countries with similar religious ideas like Japan or Tibet zero is a far more acceptable and accessible thing as so much thought there revolves around becoming one with nothingness and infinity at once.
So... what is zero... in some ways it is an interger without value, in other ways a value of no size. It is essentially a convenient way of notation of nothingness.
In a less mathamatical way it is easiest to consider zero to be the number of slices of cake left after a hungry fat man finds the cake tin...

Answer 4

Early civilizations had no concept of nothing. This concept became necessary with place notation, so that one can distinguish between 104 and 14. Since then zero has been a basic concept in mathematics. It can be thought of as the empty set, with 1 = {0}, 2 = {0,1}, and so forth. It is the additive identity in abelian groups; in other words, that element 0 such that 0+a = a+0 = a for all elements of the group.

A basic rule of mathematics is that one can't divide by zero. In a sense, you could divide a non-zero by zero, with the result being potential infinity. So infinity and zero are both the unreachable, in largeness in one direction and smallness in the other. And calculus is concerned with what happens when quantities approach zero.

A good book to read on this is Charles Seife's "Zero" - an entire book written about 0.

Answer 5

When working with natural numbers, the basic operations are addition and multiplication. Now when you multiply, the number 1 has the special property that

1 * x = x

for every x. It is a neutral element. For addition, there is no such natural number. However, we can *define* a neutral element for addition; this defines zero.

0 + x = x

This defines zero algebraically. It is a "number" because it can be combined with the other, natural numbers, without violating their essential properties.


Zero can also be defined topologically, as the limit of a sequence of ever smaller positive fractions. (By the way, are fractions "numbers"? Similar question!) Thus,

100, 10, 1, 0.1, 0.01, 0.001, 0.0001 etc.
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128 etc.

are "Cauchy sequences" as the numbers get closer and closer to another. It is very natural now to define their limit as a number -- zero. This is, by the way, the same method by which the real numbers (including e and pi) are defined traditionally (Dedekind construction).

Answer 6

Hi. Zero is the absence of value. This is a line from the movie "Stand and Deliver" but is a true statement. Think of the number 10. What does the "0" stand for? The absence of value in the "units" column. Zero is also unique because it's the only number you cannot divide any number by.

Answer 7

In the group of integers under addition,
0 is the identity element. That is, for every
integer in the group, a + e = a where e is the identity
element. Zero fits that role.

By the way, at absolute zero atoms still move.
It's called Brownian motion (you can't make them
sit completely still)

Answer 8

Absolute 0 is the temperature the position there is the bottom (yet no longer 0) thermal skill in the equipment. the version between pi and absolute 0 is that for pi there's a mathematical formulation that permits computation to any variety of digits. actual parts, on the different hand, are determined merely with suggestions from mathematical formulation. the most precise actual measurements are for quantum electrodynamics the position the blunders is below one area in 10^15. it really is an identical because the width of a hair compared to the area between la and ny. even if, it remains a techniques a lot less precise than the computations for pi or e, which do no longer ought to tournament some actual length.

Answer 9

It's a symbol representing origin (imagine a number line as a 1 dimensional graph). By scientific notation, the origin is 1. When you calibrate a scale, you set a point to relative 0.

Answer 10

well, all successful number systems need the concept of zero for calculations to be made possible, just try using roman numerals to add up or find the square root of

also, just like infinity is unachievable so too is zero in some respects, such as absolute zero. so although we naively think of it as an absence or as just a symbol, without it we are screwed. i suppose everyone has their own image of what zero / infinity is