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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.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Basics: Limit of a function

Voice

Voice

Home

Two Concepts as Numbers

»  Undefined Large
→  oo infinity
→  very large value denoted by a symbol

»  Indeterminate Value
→  0/0
→  represented by an expression
→  other forms: oo/oo, oo-oo, 0^0, 0xx oo, or oo^0

»  All the following can be true
→  0/0 = 0
→  0/0 = 1
→  0/0 = oo
→  0/0 = 6 or 8 or -3

Rigorous arithmetic calculations may result in 0/0, but the expression may take some other value. The objective of limits is to find that value.

### Indeterminate value and Undefined Large

plain and simple summary

nub

plain and simple summary

nub

dummy

oo - undefined large
0/0, oo/oo, oo-oo, 0^0- indeterminate value.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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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.

Keep tapping on the content to continue learning.
Starting the page "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.

What is the value of 1/0?

• 1
• 0
• oo

The answer is 'oo'. Infinity.

What is infinity oo called as?

• undefined large
• indeterminate value

What does "undefined" mean?

• 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?

What is the value of 0/0?

• 1
• 0
• oo
• 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
• 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
• 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

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

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

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

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

What does "indeterminate" mean?

• 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?

What is the value of oo/oo?

• 1
• oo
• 0
• 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
• 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

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
• 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

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.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

What is oo called?

• undefined large
• indeterminate value

What is 0/0 called?

• undefined large
• indeterminate value

Progress

Progress

What is the value of 1 by 0?
1
1
0
0
infinity
infinity
What is infinity called as?
undefined;large
undefined large
indeterminate;value
indeterminate value
What does "undefined" mean?
specified;assigned;value
not specified; not assigned a value with
considered;to;true
not considered to be true
The answer is 'not specified; not assigned a value with'
What is infinity called as?
undefined
What is the value of 0 by 0?
1
1
0
0
infinity
infinity
can;not;be;b;cannot
cannot be computed
The answer is 'cannot be computed' ;; Why the value of 0 by 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
6
2
2
1
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 by 0
can;not;be;b
cannot be mathematically expressed
The answer is "0 by 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
1
0
0
infinity
infinity
can;not;be;b;cannot
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
1
0
0
infinity
infinity
can;not;be;b;cannot
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
1
0
0
infinity
infinity
can;not;be;b;cannot
cannot be computed
The answer is "infinity" ;; 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
1
0
0
infinity
infinity
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 by 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 by 0? ;; 0 by 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 by 0 called?
undefined;large
undefined large
indeterminate;value
indeterminate value
What does "indeterminate" mean?
cannot;not
cannot be determined; cannot find the value of
absolutely;find
absolutely determined; find the value of
The answer is 'cannot be determined; cannot find the value of'
What is 0 by 0 called?
indeterminate
What is the value of infinity by infinity?
1
1
infinity
infinity
0
0
indeterminate;value
indeterminate value
The answer is 'indeterminate value'. ;; The answer can be explained with infinity by infinity ;; equals 1 by 0 divided by 1 by 0;; equals 1 by 0 multiplied 0 by 1 ;; equals 0 by 0
What is the value of infinity multiplied infinity?
1
1
infinity
infinity
0
0
indeterminate;value
indeterminate value
The answer is 'infinity'. ;; The answer can be explained with ;; infinity multiplied infinity;; equals 1 by 0 multiplied 1 by 0;; equals 1 by 0;; equals infinity
What is the value of infinity minus infinity?
1
1
infinity
infinity
0
0
indeterminate;value
indeterminate value
The answer is "indeterminate value". ;; The answer can be explained with;; infinity minus infinity;; equals 1 by 0 minus 1 by 0;; equals 1 minus 1 by 0;; equals 0 by 0;
What is infinity plus infinity?
1
1
infinity
infinity
0
0
indeterminate;value
indeterminate value
The answer is "infinity". ;; The answer can be explained with ;; infinity + infinity;; equals 1 by 0 + 1 by 0;; equals 2 by 0;; equals infinity
What is the value of 0 power 0?
1
1
infinity
infinity
0
0
indeterminate;value
indeterminate value
The answer is "indeterminate value" ;; The answer can be explained with ;; 0 power 0 ;; equals 0 power 1 minus 1;; equals 0 power 1 divided by 0 power 1 ;; equals 0 by 0.
infinity is called 'undefined large' ;; 0 by 0 is called 'indeterminate value'. ;; Some authors or teachers may call infinity as 'indeterminate'. As part of this course infinity is referred to as 'undefined large' and will not be referred as 'indeterminate'. ;; Similarly, some authors call 0 by 0 as 'undefined'. As part of this course 0 by 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.
infinity - undefined large ;; 0 by 0, infinity by infinity, infinity minus infinity, 0 power 0 are indeterminate value
undefined large: infinity is very large value, not determined. ;; indeterminate value : 0 by 0 is not defined to be a single value in all mathematical models or expressions. ;; infinity by infinity, infinity minus infinity, 0 power 0 are other mathematical forms of indeterminate value.
What is infinity called?
undefined;large
undefined large
indeterminate;value
indeterminate value