Difference between denote and represent

Question

In Mathematics, a set is denoted by a capital letter and is represented by writing it in the roster form, set builder form and descriptive form.

In Physics, a vector is denoted by a letter of the alphabet or the end points of the directed line segment which is representing it with an arrow(half or full) or a bar above or a tilde(~) below and is represented by a directed line segment drawn to scale whose length represents the magnitude of the vector and whose direction represents the direction of the vector.

The dictionary says:

Denote - verb (used with object)

1.to be a mark or sign of; indicate: A fever often denotes an infection.

2.to be a name or designation for; mean.

3.to represent by a symbol; stand as a symbol for.

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Represent - verb (used with object)

1.To serve to express, designate, stand for, or denote, as a word, symbol, or the like does; symbolize: In this painting the cat represents evil and the bird, good.

2.To express or designate by some term, character, symbol, or the like:

The meaning of both the words seem similar to me

What is the difference between denotation and representation (denote and represent) and their usage? I guess that representation is some what related to description.

Answer 1

It is not uncommon for technical subjects to assign specific senses to words which would be considered close synonyms in English. For example, a thesaurus would tell you that force, power, and energy are all synonyms; while they all have distinct meanings in Physics.

In your case, denote is the word typically used in math/science to describe the symbol associated with something, (see sense 3); thus distinguishing it from represent, which is employed for diagrams and such.

In thinking that the words should be interchangeable, you might be considered guilty of genetic fallacy.

The genetic fallacy (also known as the fallacy of origins or fallacy of virtue) is a fallacy of irrelevance where a conclusion is suggested based solely on someone's or something's history, origin, or source rather than its current meaning or context.

_{Wikipedia (emphasis mine)}