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I am learning about functions in mathematics. I saw the following as a video title on YouTube.
The intuitive idea of a function.
Please explain the use of the definite article the before "intuitive" and and an indefinite article a before "function".
Comments  

He has a previous video called "Formal Definition of a Function using the Cartesian Product". He wants to contrast his present video with that one, not a formal definition but an intuitive idea.

A function is a well-defined thing. By using the definite article, he is suggesting that there is no more than one way of conceiving of it intuitively, since it is such a narrow idea. He chose the indefinite article because the definite article sounds like he has a particular function in mind, and he does not. The definite article would be grammatical and, well, functional, but the indefinite is clearer.