The two important numbers "Indeterminate value" and "Undefined large" are explained. It is crucial to understand these two numbers to understand limit of a function.

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The value of `1/0 = oo`

`oo` is called "undefined large".

The word "undefined" means: not specified; not assigned a value with.

*familiarize with the terminology *

undefined large value

The value of `0/0` cannot be computed. br />

Why the value of `0/0` cannot be computed? This is explained in detail in the following pages.

Consider the division as giving out cookies to kids. If there are `6` cookies and one gives out `2` cookies to each kid, then `6/2 = 3` kids will get the cookies.

Consider the following. If there are `0` cookies and one gives out `0` cookies to each kid, then the mathematical expression for this is `0/0`.

There are `0` cookies in a cookie jar and Person A give out `0` cookies to each kid. Person A stops giving out cookies if there are `0` cookies in the cookie jar.

when starting, Person A checks the number of cookies and immediately stops giving the cookies. *In this particular case*, `0/0 = 0`.

There are `0` cookies in a cookie jar and Person B gives out `0` cookies to each kid. Person B checks if the number of cookies to be given is same as the number of cookies in the cookie jar. When those are equal, Person B gives all the cookies and stops the distribution.

When starting, Person B checks the number of cookies and finds that it matches to the number of cookies to be given out. So she gives once and stops. *In this particular case*, `0/0 = 1`.

There are `0` cookies in a cookie jar and Person C gives out `0` cookies to each kid. Person C stops the distribution only when she cannot give what a kid is to be given.

For every kid, Person C checks if she has `0` cookies. She decides, `0` cookies can be given, and so keeps on with the distribution forever. *In this particular case*, `0/0 = oo`

There are `0` cookies in a cookie jar and Person D gives out `0` cookies to each kid. Person D stops the distribution, only when she cannot give what a kid is to be given. In addition to that, Person D checks if the jar is empty, every time, after servicing 6 kids. If she finds it empty, she stops.

After giving to 6 kids, she checks if the jar is empty for the first time. Since the jar is empty, she stops. *In this particular case*, `0/0 = 6`

There are `0` cookies in a cookie jar and and one gives out `0` cookies to each kid. How many kids will receive?

This problem is mathematically `0/0`. What is the answer to this?

• Person A came with answer `0`.

• Person B came with answer `1`.

• Person C came with answer `oo`.

• Person D came with answer `6`.

So, what is the value of `0/0`?

`0/0` is named as 'indeterminate value', as it can take any value depending on the problem at hand and the process followed in solving the problem.

`0/0` is called "indeterminate value".

The word "indeterminate" means: cannot be determined; cannot find the value of.

*familiarize with the terminology *

indeterminate

Consider `color(deepskyblue)(oo)/color(coral)(oo)`

`quad quad = color(deepskyblue)(1/0) -:color(coral)(1/0)`

`quad quad = color(deepskyblue)(1/0) xx color(coral)(0/1)`

`quad quad = 0/0`

That is, `oo/oo` is "indeterminate value".

Consider `color(deepskyblue)(oo) xx color(coral)(oo)`

`quad quad = color(deepskyblue)(1/0) xx color(coral)(1/0)`

`quad quad = 1/0 `

`quad quad = oo`

That is, `oo xx oo = oo`

Consider `color(deepskyblue)(oo) - color(coral)(oo)`

`quad quad = color(deepskyblue)(1/0) - color(coral)(1/0)`

`quad quad = (color(deepskyblue)(1)-color(coral)(1))/0`

`quad quad = 0/0`

That is, `oo - oo` is "indeterminate value".

Consider `color(deepskyblue)(oo) + color(coral)(oo)`

`quad quad = color(deepskyblue)(1/0) + color(coral)(1/0)`

`quad quad = 2/0`

`quad quad = oo`

That is, `oo + oo = oo`

Consider `0^0`

`quad quad = 0^(1-1)`

`quad quad = 0^1 -: 0^1`

`quad quad = 0/0`

That is `0^0` is, indeterminate value.

`oo` is called 'undefined large'.

`0/0` is called 'indeterminate value'.

Some authors or teachers may call `oo` as 'indeterminate'. As part of this course `oo` is referred to as 'undefined large' and will not be referred as 'indeterminate'.

Similarly, some authors call `0/0` as 'undefined'. As part of this course `0/0` is referred to as 'indeterminate value' and will not be referred as 'undefined'.

Students may note that, this is a matter of nomenclature. This course adds the additional information 'large' and 'value' to give additional clue on what is being referred to.

`oo` - undefined large

`0/0`, `oo/oo`, `oo-oo`, `0^0`- indeterminate value.

**undefined large: **`oo` is very large value, not determined. **indeterminate value : **`0/0` is not defined to be a single value in all mathematical models or expressions.

`oo/oo`; `oo - oo`; `0^0` are other mathematical forms of indeterminate value.

*Solved Exercise Problem: *

What is `oo` called?

- undefined large
- undefined large
- indeterminate value

The answer is 'undefined large'.

*Solved Exercise Problem: *

What is `0/0` called?

- undefined large
- indeterminate value
- indeterminate value

The answer is 'indeterminate value'.

*switch to interactive version*