What is deductive and inductive reasoning? As a beginner to logic, I have read several explanations of inductive vs deductive reasoning, but most tend to really be explaining the same thing twice and are not found on MSE. I am looking for a thorough explanation that will make me it not only clear what the differences are, but what induction and deduction actually are on their own. Please do not, for example, refer only to mathematical induction, as this is an application of inductive reasoning.
There is one potential duplicate found here, however, the accepted answer is unsatisfactory as it does not address the question(or this question).
Difference between Deduction and Induction
 A: Mathematical induction is an axiom of the natural numbers. It forms a part of the deductive reasoning of mathematics and is a distinct thing from inductive reasoning.
With that disclaimer, let's get into the two terms.
Deductive reasoning is the sort of reasoning done in logic or in mathematics. You have a set of premises and a set of rules of logic, from that you can derive other statements entailed by your premises. An example which typifies this kind of reasoning is this:
Assume you know that "Every man is mortal" and "Socrates is a man" then deductive reasoning allows us to deduce that "Socrates is mortal".
Here we uses the role of logic called universal instantiation. The point is that we deduced using logic a conclusion from our premises. Further, we are very certain in our conclusion, as it follows necessarily from the premises.
Inductive reasoning is a very different beast. Inductive reasoning is typified by the following example:
Suppose every goose you observe throughout your lifetime is white. You then conclude that every goose is white.
This is an inductive conclusion. Note that this conclusion is not 100% definite. Just because you haven't seen a black goose doesn't guarantee their nonexistence. But if you've seen millions of geese, and all have been white, you might be fairly confident in claiming there are no non-white geese. Inductive reasoning can be described as "generalizing your past experience to universal statements", i.e. taking statements of the form "every $x$ I have experience with is $y$" to "all $x$ are $y$".
Now there are two things worth remarking on. First, mathematics entirely relies on deductive reasoning. Mathematical induction is just a name given to a certain deductive principle. Second, inductive reasoning is not definite and is considered philosophically problematic; on the other hand it forms a basis for the scientific process. Read more about that here.
