March 24, 2017 Friday

Bedtime Story 

The Language of Mathematical Logic

One of the important notation among the quantifier is the turned A or ∀.

This turned A in a sans-serif fond today is the universal quantifier that signifies “given any” or “for all”.

The other famous quantifier that he came up with was the existential quantifier.

It is denoted by the turned E or ∃ . 

This existential quantifier implies “there exists” or “there is at least one” or “for some”.

All this may seems very alien as mathematical logic is the least taught subject in high school curriculum or that was the way it used to be when I was in the school.

Then Gottlob Frege developed the idea of predicate.

Predicate as I had discussed in one my bedtime stories is a function that can be true or false depending on its value.

One can consider predicate to be a property of certain variable say x.

This is written mathematically as P(x).

Here the, x becomes a predicate variable.

So now we have three new terminologies, namely quantifiers, predicate and predicate variable.

Quantifiers are used together with predicate variables.

Let me give you an example here.

Suppose you want to say that there exists a natural number such that when it is multiplied by itself, it results in 36.

In mathematical logic, it is written as:

∃n∈P(n,n,25)

The symbol ∈ means element of or in.

This symbol establishes the relationship.

So if I wish to say that “x is an element of A”, I would write:

x ∈ A

The inverse of it would be is that “A contains x”.

That is stated as:

A ∋ x

There is also a negation of the set membership.

So to say that x is not an element of A, we write:

x ∉ A

Further, he introduced what is known as material conditional.

We shall take up the material condition in the nights to come.

Isn’t it fun mon ami?

It is just like learning a whole new language.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.in/

                              

Good night mon ami and my fellow cousin ape.

                   

  

                

             

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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg