Question

I am studying 'What is function ?' in wikipedia but I have ambiguity in so I can't understand a line ....."Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept. " I can't understand the line in bracket so if you can please help.

Answer 1

Answer:A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. ... We can write the statement that f is a function from X to Y using the function notation f:X→Y.

Step-by-step explanation:

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Answer 2

Mathematical Words

• Differentiation

→ Differentiation is the process of finding the derivative.

• Calculus

→ A part of math that deals with functions.

• Set

→ A part of math that sorts objects into belong or not belong.

Now let me explain the words.

• Functions were originally the idealization of how a varying quantity depends on another quantity.

We can write down a pattern with mathematical equations.

Let us consider $\sf{y=x-2}$.

In this function, y varies according to x.

• For example, the position of a planet is a function of time.

Graphically, you can draw the movement with a function.

For example, $\sf{y=-x^2}$ is a movement of a falling object!

• Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).

After the development in the calculus, the concept was elaborated.

• The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.

Here are the examples of set theory.

1. range and domain.
2. inverse function.
3. composite function.

The Meaning

Functions were elaborated with the calculus and the set theory.