Question

@ganeshie8

Answer 1

Prove using induction that x+3=5x for all real values of x. (This is a question I made up just to see how are we suppose to use induction upon false statements)

Answer 2

It is not possible to prove a false statement using induction or any other proof method. You would fail if you tried.

Answer 3

Yeah I know, I just want to see how is the question going to be disproved

Answer 4

You may simply show a counterexample.

Answer 5

But still I want to know how induction proofing workouts on false statement. (Like what if a statement is there for which I cant work out the authenticity of the statement

Answer 6

Like first we will assume x+3=5x to be true and then we can check for this assumption by using x = 3/4.
Then I will try to show the statement (x+1)+3=5(x+1) to be true by making algebraic manipulation in our hypothesis. Right?

Answer 7

We must have a high confidence about the validity of the proposition before applying induction.

Answer 8

What if they just say determine p=>q is true or false? (which coincidentally works out for all real values of x except 1,2 special values). What method am I supposed to adopt here?

Answer 9

Also the usual induction method doesn't work on real numbers

Answer 10

Why not?

Answer 11

Have you gone through the proof of induction method ?

Answer 12

Yes, even applied sometimes

Answer 13

The simplest and most common form of mathematical induction infers that a statement involving a natural number n holds for all values of n.

https://en.wikipedia.org/wiki/Mathematical_induction

Answer 14

Oh but still that doesn't answer my question. What if they just say determine p=>q is true or false? (which coincidentally works out for all natural values of x except 1,2 special values). What method am I supposed to adopt here?

Answer 15

Your question isn't clear. What are p and q ?

Answer 16

They are just statements

Answer 17

You're free to adopt any method as long as you know how to follow the rules

Answer 18

Oh okay. Can you just check my working for a question of proof?

Answer 19

Sure..

Answer 20

http://openstudy.com/study#/updates/57a00d74e4b0a26917e5e11d