Saturday, April 22, 2017

April 22, 2017 Saturday

Bedtime Story 


On Necessary Truths or Logical Truths


The point that I am trying to emphasize that in building up mathematical proofs, we often use assumptions or rules of inference that are never explicitly stated but implicitly assumed.

Let us go back to the proof of Euclid and consider the statement:

“Then q can either be a prime or not be a prime”.

From where did we get this statement from?

Is it not possible that q need not be either a prime or not a prime?

Here let me take you to one of the most fundamental concept in logic which formally we were never schooled.

It is the concept of necessary truth or logical truth.

A necessary truth or a logical truth is a statement that is true and remains true under all reinterpretations of its components other than its logical constants.

Let me tell you something about logical constants.

Logical constants are components of formal language (denoted by symbol  that goes by the name Laplace transform) systems that will have the same semantic value under every interpretation of that language.

Let me enlist some symbols of logic that are treated as logical constants.

Symbols                              Meaning in English

T                                         “true”

F                                         “false”

¬                                        “not”

∧                                          “and”

∨                                          “or”

→                                         “implies”, “if…then”

∀                                         “for all”

∃                                          “there exists”, “for some”

=                                          “equals”

◻                                          “necessarily”

◊                                                                   “possibly”

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:


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


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


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