Python closures for beginners python tutorial

certainly! a closure in python is a function object that has access to variables in its enclosing lexical scope, even when the function is executed outside that scope. closures allow you to encapsulate behavior and maintain state without using global variables.

### understanding closures in python

to understand closures, let's first look at nested functions. a nested function is a function defined inside another function. a closure occurs when a nested function captures the local variables of the outer function.

### key concepts

1. **nested functions**: functions defined within other functions.
2. **free variables**: variables that are not bound to a value in the local scope of the function but are accessible due to the closure.
3. **state retention**: closures can retain the state of variables even after the outer function has finished executing.

### creating a closure

here's a step-by-step guide to creating a closure in python:

1. define an outer function that includes a variable you want to retain.
2. define an inner (nested) function that uses the variable from the outer function.
3. return the inner function from the outer function.

### code example

let’s look at an example that demonstrates how closures work.

### explanation of the example

1. **outer function `make_multiplier(factor)`**: this function takes a parameter `factor` and defines an inner function `multiplier(x)`.
2. **inner function `multiplier(x)`**: this function takes a parameter `x` and returns the product of `x` and `factor`, which is defined in the outer function.
3. **returning the inner function**: the outer function returns the inner function `multiplier`, creating a closure that retains the value of `factor`.
4. **creating closure instances**: when you call `make_multiplier(3)`, it returns a new function `multiply_by_3` that has `factor` set to 3. similarly, `make_multiplier(5)` returns `multiply_by_5` with `factor` set to 5.

### benefits of using closures

1. **encapsulation ...

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