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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsLimit of a functionBasics: Limit of a function

Indeterminate value and Undefined Large

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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What is the value of `1/0`?

  • `1`
  • `0`
  • `oo`
  • `oo`

The answer is '`oo`'. Infinity.

What is infinity `oo` called as?

  • undefined large
  • undefined large
  • indeterminate value

The answer is 'undefined large'.

What does "undefined" mean?

  • not specified; not assigned a value with
  • not specified; not assigned a value with
  • not considered to be true

The answer is 'not specified; not assigned a value with'

What is infinity `oo` called as?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'undefined large value'

What is the value of `0/0`?

  • `1`
  • `0`
  • `oo`
  • cannot be computed
  • cannot be computed

The answer is 'cannot be computed'

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 how many kids will get the cookies?

  • `3`
  • `3`
  • `6`
  • `2`
  • `1`

The answer is '`3`', as `6/2 = 3`.

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

  • `0/0`
  • `0/0`
  • cannot be mathematically expressed

The answer 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. Then how many kids will receive the `0` cookies from person A?

  • `1`
  • `0`
  • `oo`
  • cannot be computed
  • cannot be computed

The answer is '`0`'.

when starting, Person A checks the number of cookies and immediately stops giving the cookies.

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. Then how many kids will receive the `0` cookies from Person B?

  • `1`
  • `0`
  • `oo`
  • cannot be computed
  • cannot be computed

The answer is '`1`'.

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.

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. Then how many kids will receive the `0` cookies from Person C?

  • `1`
  • `0`
  • `oo`
  • cannot be computed
  • cannot be computed

The answer is '`oo`'.

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.

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. Then how many kids will receive the `0` cookies from Person D?

  • `1`
  • `0`
  • `oo`
  • `6`
  • `6`

The answer is '`6`'

After giving to 6 kids, she checks if the jar is empty for the first time. Since the jar is empty, she stops.

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.

What is `0/0` called?

  • undefined large
  • indeterminate value
  • indeterminate value

The answer is 'indeterminate value'.

What does "indeterminate" mean?

  • cannot be determined; cannot find the value of
  • cannot be determined; cannot find the value of
  • absolutely determined; find the value of

The answer is 'cannot be determined; cannot find the value of'

What is `0/0` called?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'Indeterminate Value'

What is the value of `oo/oo`?

  • `1`
  • `oo`
  • `0`
  • indeterminate value
  • indeterminate value

The answer is 'indeterminate value'.

The answer can be explained with
`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`

What is the value of `oo xx oo`?

  • `1`
  • `oo`
  • `oo`
  • `0`
  • indeterminate value

The answer is '`oo`'.

The answer can be explained with
`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`

What is the value of `oo - oo`?

  • `1`
  • `oo`
  • `0`
  • indeterminate value
  • indeterminate value

The answer is 'indeterminate value'.

The answer can be explained with
`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`

What is the value of `oo + oo`?

  • `1`
  • `oo`
  • `oo`
  • `0`
  • indeterminate value

The answer is '`oo`'.

The answer can be explained with
`color(deepskyblue)(oo) + color(coral)(oo)`
`quad quad = color(deepskyblue)(1/0) + color(coral)(1/0)`
`quad quad = 2/0`
`quad quad = oo`

What is the value of `0^0`?

  • `1`
  • `oo`
  • `0`
  • indeterminate value
  • indeterminate value

The answer is 'indeterminate value'.

The answer can be explained with
`0^0`
`quad quad = 0^(1-1)`
`quad quad = 0^1 -: 0^1`
`quad quad = 0/0`

`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'.

                            
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