Question

- so the collatz's conjecture said ,,... if is even divide by 2 and if is odd multiplie by 3 and add 1 .... so to the end allways will result 1.

example.

1*3 +1 = 3+1=4 what is power of 2 so what mean that dividing by 2 =2/2 =1 so we get 1
2 is even so 2/2 =1
3 odd so 3*3 +1 = 10 even so 10/2=5 what is odd so 5*3 +1 = 16 what is power of 2 what mean that on the end will result 1
4=2^2 so will result 1
5 odd so 5*3+1=16 = 2^4 power of 2 so will result 1
-so than we need proving that in case of every odds will result power of 2 using this method

prove that allways will be a natural number n for what (2n+1)*3 +1 will result power of 2

Answer 1

(2n+1)*3 +1 A statement ........ equals what?

Answer 2

yes i like continue it here

every odds we can writing in the form of 2n+1

yes ?

so (2n+1)*3+1=6n+3+1=6n+4 =2(3n+2) so what mean that in case of every odds we will get like result even

Answer 3

so for we can proving the collatz"s conjecture we need proving that using this method of dividing by 2 when is even and multiplying by 3 and adding 1 when is odd so in this case on the end will result allways power of 2

(2n+1)*3 +1 = 6n +3 +1 = 6n +4 = 2(3n +2) /2 = 3n +2

so for we can proving what we have wrote above us reductio add absurdum method

suppose that 3n+2 not equale never power of 2

but for n=2 we get 3*2 +2 = 8 = 2^3

Q:E:D:

opinions please ! thank you very much

Answer 4

@saifoo.khan
@satellite73
@dumbcow
@ganeshie8

Answer 5

@ash2326
@sauravshakya

Answer 6

@Hero

Answer 7

well you have just proved following statement wrong:
for all n , (3n+2) can never be written as power of 2.
but this does not prove collatz conjecture

Answer 8

Actually once I also tried to think on this problem....... approached from various ways but got nothing....... I guess if u prove after some steps u will always reach a smaller number than a number that u started with then it will prove the conjecture

Answer 9

ty

but if you check it for an standard form of odd numbers why you not can using the reductio add absurdum method of ,... and why not can being this accepted ?

Answer 10

what do you mean by reductio add absurdum method?

Answer 11

what have wrote there

because (2n+1)*3+1 will result allways even what divide by 2 we get 3n+2 so this 3n+2 suppose not will be never power of 2 but for n=2 we get 8 = 2^3

Answer 12

@Hero
@ash2326
@radar
@dumbcow

opinion

Answer 13

@amistre64

Answer 14

@cwrw238 opinion

Answer 15

@jim_thompson5910

Answer 16

Sorry my opinion does not count.

Answer 17

but do you understand this proof by reductio add absurdum ?

Answer 18

and how is possibille that ,,persons with title of champion dont know the reductio ad absurdum proof method ?

Answer 19

it's typically called proof by contradiction

Answer 20

@oldrin.bataku yes i think that you see it right but when i have learned this was the name of this proof method -- reductio ad absurdum -- yes ,what mean proof by contradiction

ty

...and what is your opinion from this proof by contradiction ? you see it correct or ...?...
your opinion ?

Answer 21

I think you are misinterpreting the Collatz conjecture

Answer 22

how do you think this and why ?

Answer 23

Collatz said

Answer 24

take indifferent number : than even divide it by 2 than odd multiplie it by 3 and add 1 so the final result will be allways 1

yes ?

Answer 25

@radar you see it the same too ? please what is your opinion from ?

Answer 26

Yes, for example if the number was 9, the sequences would be 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 at least I know that one does, but I don't know if there may be a number where it won't go that way.

Answer 27

Like a real large number, as they have tested numbers way way way up there, and so far the sequence has gone to 1.

Answer 28

I would assume a negative number would terminate at -1, still a 1 (I think)

Answer 29

Gotta run, my meat loaf is ready.

Answer 30

some numbers take a lot of steps to terminate

e g n=27 takes 111 steps before reaching 1
others , a lot longer

like the Riemman hypothesis this is one of the conjectures that hasn't been proved yet

Answer 31

proof by contradiction is powerful technique

you start by assuming the opposite of the hypothesis is true
eg to prove that sqrt 2 is irrational assume that it can be written as a/b (that its rational)
then by using logical steps you come to a statement that cannot be true (thats absurd - hence the 'redact ad absurbium.')

thus you conclude that your assumption cannot be correct
therefore the original hypothesis must be true

if you look up this proof you'll see the details

in the case of collasz conjecture you'd start by assuming the process can result in a number other than 2

Answer 32

* other than 1

Answer 33

ty

so than like finaly result you consider it proven by reductio ad absurdum method ?

Answer 34

i dont know - i'll have to look at it later no time now

Answer 35

if you assume 3n+2 is not a power of 2 for all natural numbers and use contradiction method, then you are just proving there exist at least one integer n for which 3n+2 is a power of 2

Answer 36

right