Defined Recursion (#27605)

* Defined Recursion

Added an English definition for recursion with examples and external sources.

* md-ize and format

guide/english/mathematics/functions/recursively-defined-functions/index.md

@@ -9,7 +9,59 @@ This is a stub. <a href='https://github.com/freecodecamp/guides/tree/master/src/
 
 <!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds  -->
 
+### A Quick Intro
+
+Put simply, recursion if a form of defining something using itself within the definition
+
+This is a common example used to teach recursion, a function to generate the fibonacci numbers:
+``` 
+f(0) := 0  Base case 0
+f(1) := 1  Base case 1
+f(x) := f(x - 1) + f(x - 2) | x > 1
+```
+
+Now, defining a function with itself will leave you with a few problems. The biggest is that if you define a function with itself, how are you supposed to know/determine when the function stops? 
+
+Here's a simple example:
+```js
+function foo(x){
+  y = x + 1;
+  console.log(y);
+  foo(y);
+}
+```
+
+This function takes some number, and adds 1 to it infinitely. 
+In order to determine a stopping point, you need to add a base case.
+
+A base case is a point at which the function does not call the recursive step. 
+
+```js
+function foo(x){
+  if(x > 5){
+    return x
+  }
+  y = x + 1;
+  console.log(y);
+  foo(y);
+}
+```
+This is now equivalent to:
+
+```js
+function foo(x){
+  while(y < 5){
+    y = x + 1;
+    console.log(y);
+  }
+}
+```
+
+Almost everything that can be defined recursively can also be created with a loop. In fact, most compilers turn your code into a loop anyway, at some point, prior to it being executed.
+
+It should also be noted that recursion may look cool and allow you to shrink a long loop down into just a few lines of code but there are a few drawbacks. Mainly, performance of a recursive definition is generally slower than that of an iterative one, not to mention, it can be harder to read for people unfamiliar or new to the concept.
+
 #### More Information:
 <!-- Please add any articles you think might be helpful to read before writing the article -->
-
+- https://en.wikipedia.org/wiki/Recursion
-
+- https://introcs.cs.princeton.edu/java/23recursion/