Indeterminate form

In calculus, while computing limits of a function, you may get value like 0/0 or ∞/∞. These answers do not represent any feasible real value, and are termed as indeterminate form (from indeterminate, meaning something that is not definite).

Common indeterminate forms

0/0 is indeterminate because anything divided by itself is 1 except for 0. Zero divided by zero can not be realized or computed.

Similarly,∞/∞ is also indeterminate because infinity is a very large number, and although anything divided by itself is equal to 1, infinity divided by infinity can not be determined because we don't know how larger one infinity will be from the other.

Differences of infinity like ∞ - ∞ are also indeterminate forms, because since infinity is a very large, but unknown number, so you don't know how large one infinity is from the other, and so on subtracting it you don't know what you will get. It seems that ∞ - ∞ = 0 is correct but since you don't know exactly how large an infinity is, you can't say that they are equal and on subtracting them you will get zero.

Note that the sum of two infinities, that is ∞ + ∞, is not an indeterminate form because it is equal to ∞ That is, ∞ + ∞ = ∞ Similarly -∞ + -∞ = -∞

More indeterminate forms

Other indeterminate forms are 0^0, 1^∞, 0 * ∞ and ∞^0