Question

prove by math induction ,so n is natural ,greater than 2 , a and b natural ,that n=a+b+1 is always true

Answer 1

so you wanna prove if a,b are natural then n should be natural as well ?
mmm i dont understand what you are trying to prove :o

Answer 2

does \(N \in \{0\}\) and does \(a \ne b\) ?

Answer 3

mm you should say
does {0}∈ N
also
does a≠b mmm i cant see its a condition

Answer 4

indeed, so do you count 0 as a member of the naturals? there isnt a defined use of 0 afaik

Answer 5

I suppose it doesnt really matter since its for \(n>2\) and not \(n\ge2\)...

Answer 6

you need to prove that for every n will exist an a and b for what this equality will be true

Answer 7

lets assume it is TRUE for n=k,
k=a+b+1, where a and b are natural numbers

Now, for n =k+1
k+1=(a+b+1)+1
= (a+1)+b+1
Since a and b are natural numbers , (a+1) and b must also be natural numbers
Thus, if it holds TRUE for n=k then it also holds TRUE for n=k+1

Now,
when k=3 then
3=a+b+1
3=1+1+1 (lets choose a=1 and b=1 where both a and b are natural numbers)
3=3(TRUE)

Hence, the statement is TRUE for n>2

Answer 8

mmm

Answer 9

@ikram002p do you like this proof too or what mean ,,mmm" ?

Answer 10

ty @sauravshakya !

Answer 11

so than this is like easy how will be proven by math induction too that
m= (p-1)/2 +(q-1)/2 +1 is true

m greater than 2
p and q are odd numbers

- can prove it the same like this above ?

ty for your answer

Answer 12

@sauravshakya opinion please

ty

Answer 13

Since p and q are odd numbers they can be expressed as p=2a+1 and q=2b+1 where a and b are set of whole numbers,
(p-1)/2 = (2a+1-1)/2=a
(q-1)/2=(2b+1-1)/2=b

Answer 14

and this will be similar to the first question

Answer 15

ty

Answer 16

@ParthKohli your opinion is the same please ?

Answer 17

Yup, the proofs look good to me

Answer 18

ty

good luck

Answer 19

well i dont think that induction is good proof for the identity of sum of natural numbers is also natural . its more of abstract algebra than being a proof with induction

Answer 20

i would say (weak proof )
sorry , but this is my opinian about it
note that induction already use the identity of sum of natural number is natural so itmake no sense

Answer 21

@satellite73
@mathmale

- please your opinion about this ?

thank you

Answer 22

@ikram002p how do you think about proof by reductip ad absurdum method ?

Answer 23

@ganeshie8
@Hero

... your opinion please ?

thank you very much

Answer 24

idk what is reductip ad absurdum method , but if you wanna proof that sum ofnatural number is also natural , then u gotta use basic things , like grouping (show natural number is a group ) or using well ordering principle

Answer 25

how and what proof could better to prove this statement ?