Can anyone tell me why zero is a number and not a math operation?

Question

I know that zero works great to establish place value. However, if you owe me a dollar you can never pay it back with zeros! The way zero is used is fine; but I think it should be classed with operations and not classed as a number. What is your answer?

Answer 1

Operator:

(from en.wikipedia.org)

In mathematics, an operator is a function, usually of a special kind depending on the topic.

(from dictionary.com)

Mathematics. A function, especially one from a set to itself, such as differentiation of a differentiable function or rotation of a vector.

(from mathworld.wolfram.com)

An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on the real line or in the complex plane, the mapping is usually called a functional instead.

The bottom two definitions are a little more technical, but they all contain the core of what an operator is: It is a *function* that takes one or more parameters and gives an output.

For example, '+' is an operator because it takes two parameters and outputs their sum. '-' is an operator because it takes two parameters and outputs their difference. '!' is an operator because it takes one parameter and outputs the factorial of that parameter.

Zero is a number. It is not a function that takes parameters, performs changes, and provides an output. In fact it *is* a parameter that can be used by operators itself:

0 + 2
5 - 0
0!

If you are still confused, try thinking of what operations or what functions zero performs on other numbers. Don't say place-holding, because that's not changing the number, it's just representing it, just like 1, 2, 3, etc. represent the number. I believe that you will find that zero does not perform operations on other numbers, but instead is just a very special and important number in our number system that can be used by operators like any other number.

Answer 2

Arabic numbers (which were invented long ago in India, despite the name; I believe they are called that because Europeans first learned them from Arabic traders) are basically abbreviated polynomials. For example, 1230 = 1*10^3 + 2*10^2 + 3*10^1 + 0*10^0. The zero is this example is there not only to hold the place value, but to indicate that there are no units in the quantity I am trying to express. If you expressed the number without zero, you would have to indicate the degree of each of the other coefficient (which would require more writing). You could choose another symbol to indicate that there are no units, but that symbol would ultimately replace zero. So, there is no easy way to get rid of zero as a number in our number system. I do not believe anything could be gained from making it obsolete either.

The number zero was not invented by the Babylonians as another answerer suggested, although they had a place-holding symbol that perfomed some of the functions of zero: http://en.wikipedia.org/wiki/0_%28number%29#Prehistory_of_zero

Answer 3

Well before zero was 'invented' in India in the 1800s, the math world was very confused, they did not know the transition between positives and negatives, and could not create symbols (Arabic numerals are used nowadays - e.g. 1, 2...) for numbers larger than 9. Numbers are defined as values, and zero is also a value. Technically, it is actually the absense of a value, because its value is nothing, but if a value can be put to zero, then yes, zero is a number.

Answer 4

well zero is a place hold, 0 is nothing, put a one in front and it becomes 10 , two zeros is 100, so technically, with out zero, someone that owed you money would only be able to give you back a max of nine dollars, so zero before one has no value, but idealistically, when you start getting into 10's , 100's , 1000's ....zero has quite a great value....but thats just my opinion

Answer 5

IT would be pretty weird having zero as a math operation... I mean, 3 0 5? come on, puh-leeze!

And zero was NOT invented by India in the 1800's. It was invented by the Babylonians around 3000 BC.

Answer 6

The problem is, it IS a number. I can count with 0. I can say I have 0 apples, and I may be right. I can't say I have + apples, because + is an operator, not a number.

The same logic could be applied to the negatives. I can never pay you back a dollar with negatives, but that doesn't mean that they should be classed as operators.

Answer 7

Read about how natural numbers can be constructed using the Peano Axioms.

Natural number
http://en.wikipedia.org/wiki/Natural_number

Note that natural numbers have a very weak structure. There is something like an order and a first element but it is quite arbitrary where you start to count. To do something useful with these numbers one would have to introduce operations. Addition and Multiplication are well defined on the set of natural numbers. But what about neutral or inverse elements? They aren't elements of this set.

Identity element
http://en.wikipedia.org/wiki/Identity_element

Inverse element
http://en.wikipedia.org/wiki/Inverse_element


The set theoretical approach to solve this is using equivalence classes to build more general sets out of already constructed ones. Equivalence classes can be defined by binary operations on these sets.

Equivalence class
http://en.wikipedia.org/wiki/Equivalence_class


For example: The negative numbers can be constructed as the set of equivalence classes of ordered pairs (a,b) of natural numbers {1,2,3, ...}, where the equivalence relation is defined by

(a,b) ~ (c,d) if and only if a + d = b + c

Here the equivalence class of the pair (a,b) can be identified with number a - b.

.
.
.

3 := [(4,1)] = {(4,1), (5,2), (6,3), ...}

2 := [(3,1)] = {(3,1), (4,2), (5,3), ...}

1 := [(2,1)] = {(2,1), (3,2), (4,3), ...}

0 := [(1,1)] = {(1,1), (2,2), (3,3), ...}

-1 := [(1,2)] = {(1,2), (2,3), (3,4), ...}

-2 := [(1,3)] = {(1,3), (2,4), (3,5), ...}

-3 := [(1,4)] = {(1,4), (2,5), (3,6), ...}

-4 := [(1,5)] = {(1,5), (2,6), (3,7), ...}

.
.
.

Voilà, the Integers. Weird but well defined. So, one can say zero is not a natural number, it arises from the definition of an additive operation on the set of natural numbers. The same approach yields the rational numbers by introducing the multiplicative operation. The real numbers can be considered as equivalence classes of Cauchy sequences of rational numbers.

Construction of real numbers
http://en.wikipedia.org/wiki/Construction_of_real_numbers


PS: Note the extensive use of the word 'can'. All properties of numbers can just as well be set axiomatically.

Answer 8

When i read this this is what came to my mind!
If you have a whole bunch of zeros it still equals nothing altogather....100 zeros nothing at all...how can 0+0=O
Whats the point of doing that! Nothing always= nothing unless it collapses and becomes something which would be a postive or negative making nothing the orgin of everything or zero the start of every number. tee he!

Answer 9

Yes, the zero was invented in India, but not in the 1800s, ya dumbass

Answer 10

ZERO IS A ZERO IF ZERO HAD A ZERO OF THE VALUE ZERO WITHOUTH ANY ZERO.
SO WHY THINK OF ZERO .LIFE IS ZERO WITHOUTH A ZERO . SO ADD MANY ZEROS TO THE ZEROS TO GET SOME ZEROS

BYE ZERO