What is the purpose of inductive and deductive reasoning in mathematics? And how can they help prove theorems?
2006-12-22 07:01:28 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
mathematics could not exist without inductive and deductive reasoning, the inductive system allows you to see addition, the deductive is subtraction, together we can agree that all things are inductive as a whole and deductive as a unit
2006-12-22 07:25:23 · answer #1 · answered by Unconditional Love 1 · 0⤊ 0⤋
Inductive reasoning is the derivation of general knowledge based on specific knowledge. In math, it's used to prove theorems like "1 + 2 + 3 + ... + ( n - 1 ) + n = ( n^2 + n ) / 2" using a method called "proof by induction". This is where you prove a base case (or base cases for proofs involving things like the Fibonacci sequence) and then generalize to every possible case.
Deductive reasoning is the inverse process: the derviation of specific knowledge based on general knowlege. For example, you can use the quadratic equation to deduce that the solutions for x^2 - 1 = 0 are 1 and -1.
2006-12-22 09:02:35 · answer #2 · answered by Mercutio24 2 · 0⤊ 0⤋
inductive reasoning is bottom up processing, example
what is the next number in this sequence?
1, 1, 2, 3, 5, 8, 13, ? it is 21 as each new number is the sum of the last 2.
deductive reasoning is top down processing, example
if you use Pythagorean's theorem to solve unknown side of a triangle
A sq +B sq= C sq
6" +8" =?
36 +64= 100, the sq root of 100 is 10", therefore the unknown side is 10 inches.
regarding this last example, it could be said that you used inductive reasoning to decide to use the Pythagorean's theorem to solve this problem when you saw it.
but the solution of 10" is a result of deductive reasoning
I hope this helps
2006-12-22 07:54:26 · answer #3 · answered by James O only logical answer D 4 · 1⤊ 0⤋
Inductive reasoning helps you to make a smart guess based on not too much information at hand. It is very important in scientific inquiry.
Deductive reasoning helps you to do things logically step by step.
2006-12-22 07:50:31 · answer #4 · answered by sahsjing 7 · 2⤊ 0⤋
Good question!When you work in offices and places were you work with numbers that's when math comes in.If that's NOT you're question,then I have NO clue!
2006-12-22 07:05:11 · answer #5 · answered by HSMLOVER 2 · 0⤊ 0⤋
to resolve issues.
2006-12-22 07:26:07 · answer #6 · answered by Anonymous · 0⤊ 0⤋
They can't. That's just a myth.
2006-12-22 07:04:04 · answer #7 · answered by Bestie 6 · 0⤊ 1⤋
NOTHING. THERE IS NO POINT TO MATH. EVER!
>.<
2006-12-22 07:08:31 · answer #8 · answered by Anonymous · 0⤊ 4⤋