Functions in programming

Are functions in mathematics similar to functions in programming. Am I right yes or no?

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Exactly the same.
In mathematics I give a function an input and the function does it’s “thing” and hands me back an output.

Functions are similar in programming

Think of a function that squares a number

int square(int n) {
    return n*n
}

You give the function it’s input “n”
from there the function mutates n by multiplying it by itself
it returns this new output to you.

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Not so. Similar in an anologous way, but not exact.

Functions in programming are re-usable code blocks that can take any form. In maths they refer to variation of y in terms of x.

y = f(x)

y varies as x according to the relationship defined in the equation.

f(x) = ax + b

where a and b are fixed, and x is the independent variable. When f(x) returns more than one value for y for one input of x, it is no longer a function, but a relation.

Take for instance a standard quadratic,

f(x) = ax^2

which produces a parabola centered about the original and reflected off the y axis. Each value of x yields only one value for y. If we rotate the graph 90 degrees clockwise or counterclockwise it is no longer a function since we get two values for y for one value of x.

x = ay^2

which when we solve for y, becomes,

y = +/-(x / a) ^ 0.5

As we can see, there are now two solutions.

We can write program functions that emulate maths, but that is where the similarity ends.

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Is the definition of return to give something back as an answer? Am I right yes or no?

More or less, yes. A return is the response of the function to the caller. The caller is in a scope different from the function, and return bridges the scope gap.

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