What is 1/0?

Question

I should have added this in the first place, I know it's impossible, but why?

Answer 1

Hey there!

Some teachers referred to 1/0 as undefined. According to gugliamo00's answer, he states that:

If there is a number 7, then the reciprocal of 7 is 1/7.
If there is a number 2/3, then the reciprocal of 2/3 is 3/2.

So, if we find the reciprocal of 0, we get 1/0, but we don't know the value of 1/0.

This is why 1/0 is undefined. Some people call it infinity. However, if you have learned calculus, we can use limits to prove them right or wrong.

Suppose we have the function f(x)=1/x, where x is approaching 0. Then:

f(x)=1/x -->
lim 1/x -->
x->0
R=lim 1/x
x->0+
L=lim 1/x -->
x->0-
R=infinity
L=-infinity -->
R≠L -->
limit does not exist.

In other words, draw the graph of f(x)=1/x. As the value of x is approaching 0 from the left side, the value of f(x) is approaching -infinity. As the value of x is approaching 0 from the right side, the value of f(x) is approaching infinity. Since -infinity≠infinity, the limit does not exist, meaning that there is no defined value for 1/0. So, we can't say infinity.

Contrastly, some people say the graph of f(x)=1/x^2. As we look in the graph, as x approaches 0 from the left side, f(x) approaches infinity. As x approaches 0 from the left side, f(x) approaches infinity. So, since infinity=infinity, then we can say that 1/0 is infinity.

But it depends on how we look at it. Functions such as 1/x, 1/x^3, 1/x^5, give us an undefined value. Functions such as 1/x^2, 1/x^4 and 1/x^6 give us a value of infinity.

The answers depend on how we look at it.

Hope it helps!

Answer 2

The only one with the right answer so far is J Bareil. He seems to have a pretty good grasp of mathematics.

For almost any number you come up with I can give you another number than when you multiply your number and mine you get 1
If you give me 7, I'll give you 1/7.
If you give me -2/3, I'll give you -3/2.
If you give me (3x-7)/(7x+3), I'll give you (7x+3)/(3x-7).
See how it works?

These pairs of numbers are called "multiplicative inverses" of each other. Some call them "reciprocals." And some, who don't know any better, call multiplying by the reciprocal of a number, "dividing by that number"... that is, they call multiplying by 1/7 "dividing by 7." And they think of the reciprocal of a number as "one over that number"... the reciprocal of 7 is 1/7.

Problem: I said that for ALMOST any number you give me I can come up with a reciprocal. Zero is the problem. Zero has the unique property that no matter what you multiply by zero, you get zero as the product. 0n=0 for all n. That means there's no reciprocal for zero (1/0) such that the product of (0)(1/0)=1. 1/0 is undefined. Since the reciprocal of 0 does not exist, people say, "you can't divide by 0." Now you know why.

People in Calculus play with limits. They talk about the "limit" of 1/x as x gets close to zero. You'll note that the smaller x gets, the larger 1/x gets. As we've already determined 1/0 does not exist. They call the limit "infinity." That doesn't mean that 1/0=infinity, or that infinity multiplied by zero=1. Infinity isn't defined any more than 1/0 is defined. It's just a concept... an idea.

ADDED:
If you tell you're teacher that √(-1) is undefined, you sure won’t impress him/her--at least not with your mathematical knowledge. √(-1) is defined as “i”. If you haven’t gotten there already, you will.

Answer 3

It is not possible to calculate because division, say a/b, is only meaningful if b has a multiplicative inverse. That is, there is some value c such that b*c=1. Then we define a/b = a*c. However, since 0*x = 0 for all possible x, there can't be any such c such that 0*c = 1, and so 0 does not have any multiplicative inverse, and therefore a/0 is not defined.

Answer 4

1/0
= 1 ÷ 0
= undefined

Answer 5

It is undefined, because any number times 0 is zero, so it is not possible to have any greater value.

Answer 6

In real number arithmetic, the value 1/0 has no meaning. Operations such as this one are generally referred to as "undefined".

When limits are considered, or if the operation is outside the real number system, the value a/0 is often taken to be "infinity".

Answer 7

Undefined.

Answer 8

You have just wasted 5 points for asking this.No solution for 1/0.

Answer 9

it is what is called the 'infinity'.

even 2/0, 100/0, 123542/0 are equal to infinity.

but 0/0 is called indeterminate form.

impress your teacher. ask him/her what the square root of -1 is. it is a similar question.

:)

Answer 10

officially "undefined" by the rules of mathematics.

However if you are studying calculus, specifically limits, you can say that for f(x) = 1/x as x approached zero, f(x) approaches infinity.