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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.
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.

click on the content to continue..

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

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

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

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

What is the value of oo/oo?

• 1
• oo
• 0
• indeterminate value
• 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 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 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

What is 0/0 called?