+0

# Geometry

+1
692
9

The number of black-footed ferrets has increased each year since 1985. Therefore, there will be more black-footed ferrets next year than there are this year.

Is this inductive or deductive? Why?

Nov 10, 2015

#2
+17747
+10

This is inductive because you are using the knowledge of the past to predict the future.

Induction allows for the possibility that your prediction can be wrong; what happened in the past doesn't always predict the future.

To have deduction, you must already have a rule that always works.

Because you are guessing the rule, you are using induction.

An example:

Induction:  Guess the next number in this sequence:  1, 2, 4, ___.

Deduction: The rule is double the last number to get the next number in this sequence:  1, 2, 4, ___

<For the induction example, you might guess the next number is 7 because going from 1 to 2, you add 1, going from 2 to 4, you add 2, going from 4 to the next number, you add 3, etc. For the deduction example, the only possible correct anser is 8.

So, for induction, you might have more than one 'right' answer because you might be able to create more than one rule, while, for deduction, there is only one right answer, because there is only one rule.>

Nov 11, 2015

#1
0

It is "deductive"!!!!!. Because you deduce from your statement that the number of black-footed ferrets has steadily increased each year in the past and will continue that trend into the future barring unforseen circustances.

Nov 10, 2015
#2
+17747
+10

This is inductive because you are using the knowledge of the past to predict the future.

Induction allows for the possibility that your prediction can be wrong; what happened in the past doesn't always predict the future.

To have deduction, you must already have a rule that always works.

Because you are guessing the rule, you are using induction.

An example:

Induction:  Guess the next number in this sequence:  1, 2, 4, ___.

Deduction: The rule is double the last number to get the next number in this sequence:  1, 2, 4, ___

<For the induction example, you might guess the next number is 7 because going from 1 to 2, you add 1, going from 2 to 4, you add 2, going from 4 to the next number, you add 3, etc. For the deduction example, the only possible correct anser is 8.

So, for induction, you might have more than one 'right' answer because you might be able to create more than one rule, while, for deduction, there is only one right answer, because there is only one rule.>

geno3141 Nov 11, 2015
#3
+95360
+5

Thanks Geno,

I did not know that!!     I shall try and remember.

So when we prove by induction then we are proving based on what has come before.  Mmm

It beats me why this is titled "geometry"

Nov 11, 2015
edited by Melody  Nov 11, 2015
#4
0

Mathematical induction is a mathematical proof technique, most commonly used to establish a given statement for all natural numbers, although it can be used to prove statements about any well-ordered set. It is a form of direct proof, and it is done in two steps. The first step, known as the base case, is to prove the given statement for the first natural number. The second step, known as the inductive step, is to prove that the given statement for any one natural number implies the given statement for the next natural number. From these two steps, mathematical induction is the rule from which we infer that the given statement is established for all natural numbers.

Nov 11, 2015
#5
+94558
0

Thanks, geno........the distinction between these two things always confused me, too.....!!!!

Nov 11, 2015
#6
0

The number of black-footed ferrets has increased each year since 1985. Therefore, I INDUCE there will be more black-footed ferrets next year than there are this year. RIDICULOUS GINO!!!!!!!!!!!!!!!!!!!!!!!!!.

Nov 11, 2015
#7
+95360
0

That is strong words coming from someone who will not dientify him/herself. !

Sometimes a word that is used in  the precise language of mathematics

can be used very differently to how it is used in its non-mathematical context.

Maybe another mathematician who is more knowledgable than me would like to have input here.

Nov 11, 2015
#8
+95360
0

I just read the longer ealier post made by the same of maybe  a different guest.

Paraphrasing here "Mathematical induction uses  deductive not inductive reasoning".  Yes, maybe LOL

Whoevere said mathematics can't be funny.

Nov 11, 2015
#9
0

I noticed that "Guest # 1" qualified his/her statement by saying "barring unforseen circumstances" Still "inductive?" Confused!!!!!!.

Nov 11, 2015