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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

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. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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.

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

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. continue

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. continue

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. continue

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`

*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

You are learning the free content, however do shake hands with a coffee to show appreciation.

*To stop this message from appearing, please choose an option and make a payment.*

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.

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

The answer is 'undefined large'.

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?

- Practice Saying the Answer

The answer is 'undefined large'

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

The answer is '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?

- Practice Saying the Answer

The answer is 'Indeterminate Value'

What is the value of `oo/oo`?

- `1`
- `oo`
- `0`
- 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`
- `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 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`
- `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 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.

*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

The answer is 'undefined large'.

What is `0/0` called?

- undefined large
- indeterminate value

The answer is 'indeterminate value'.

*your progress details*

Progress

*About you*

Progress

What is the value of 1 by 0?

1

1

0

0

infinity

infinity

The answer is "infinity"

What is infinity called as?

undefined;large

undefined large

indeterminate;value

indeterminate value

The answer is 'undefined large'.

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

The answer is 'undefined large'

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

The answer is '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

The answer is 'Indeterminate Value'

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

The answer is 'undefined large'.

what is 0 by 0 called?

undefined;large

undefined large

indeterminate;value

indeterminate value

The answer is 'indeterminate value'.