Why is a number divided by zero undefined?

Why is a number divided by zero undefined?

The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction. r*0=a. (1) But r*0=0 for all numbers r, and so unless a=0 there is no solution of equation (1).

Is zero divided by infinity undefined?

Zero divided by “infinity” is undefined because you have not defined “infinity” and there is not a default “infinity” for us to use.

Why is 0 divided by infinity not indeterminate?

0 < f(x)/g(x) < f(x). Hence f(x)/g(x) gets squeezed between 0 and f(x), and f(x) is approaching zero. Thus f(x)/g(x) must also approach zero as x approaches a. If this is what you mean by “dividing zero by infinity” then it is not indeterminate, it is zero.

Is 0 divided by infinity defined?

Zero divided by infinity is zero, not infinity. Any division problem with zero in the numerator is always equal to zero because even if you were to put zero into the numerator an infinite amount of times, you’d never actually reach the numerator. ∞ * 0 = 0. Therefore, 0/∞ = 0.

What is divided by infinity?

In general, any number divided by 0 equals to infinity.

Why is the value of something divided by 0 undefined?

As we cannot guess the exact number, we consider it as a length of a number or infinity. In normal cases, the value of something divided by 0 has not been set yet, so it’s undefined.

What is a number divided by 0 equal to infinity?

Undefined, because +0 = -0, so the result would be both infinity and minus infinity. But in a setting (as is usually done with complex numbers) where plus and minus infinity coincide, a number divided by 0 would be this infinity.

Is infinity the same as undefined?

If your number system includes infinity, the result is infinity. If it doesn’t, the result is undefined. Infinity doesn’t exist in the real number system but it exists in the extended reals. Is a division by zero technically infinity or undefined?

Why is division by zero considered indeterminate?

As there are no two numbers further apart than infinity and negative infinity, this indicates the answer is indeterminate and undefined. If division by zero is possible, it allows for proofs of things we know not to be true.