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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.

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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

What is 0/0 called?