Question

Give solid justification of the following statement ( figure they mean prove):

Every integer greater than 4 can be expressed as the sum of two prime numbers.

Answer 1

I'm totally new to proofs, not even sure how you would.....like give solid justification.

Answer 2

I could be wrong but I believe there is no proven rule that can be applied to prime numbers. (Oh there are a few obvious ones such as "prime numbers are never even - except for 2" or "5 is the only prime number that ends in 5".

Answer 3

Are u actually asking us to prove Goldbachs Conjecture..??..No one's done it ever dude..

Answer 4

I'm not sure what Im asking beyond what I posted. This is probably why the question said solid justification and maybe not "prove"

Answer 5

We basically were given a hw sheet with a bunch of statements on it. We were to say whether they were true or false and then give as much justification as possible. But I feel like just putting down a few examples isn't what we're supposed to do, lol.

Answer 6

The question u posted is one of the most famous conjectures( thats a statement thats never been found to be invalid untill now but there exists no proof of it) in history( this is the modified one)..called the Goldbach's Conjecture...Even Laplace or Bernoulli couldn't solve it...so I believe the statement is true but u have to be satisfied with providing examples...btw if u ever prove this conjecture u can claim a large prize some institute is ready to give

Answer 7

So I can't really go beyond a few examples then, eh?

Answer 8

Not unless u prove it on ur own...

Answer 9

Gotcha. Mind if I ask one that is a bit more....provable? xD I just want to see how to go about these I guess. I feel like my answers are all ramblings.

Answer 10

I can try..

Answer 11

Alrighty. This one isnt bad, I just dont know how id write the proof.

If x is an integer then:
\[x ^{2} \ge x\]

Answer 12

okkk...x^2>=x...for any integer thats always true...for a +ve integer other than 0 and 1u know that x^2 literally means x*x thats (x+x+x+...) x times isn't it...?? so it has to be greater than x...and for a negative integer..well u know x^2 is always positive...so if x is neg..x^2 has to be greater than x...however for 0 and 1x^2=x...so for any integral value x^2>x......is that a satisfactory proof enough?

Answer 13

I can use it for ideas to try and add or alter what I have. I don't know whats a solid proof yet, so anything helps that can make me feel stronger about my argument xD

Answer 14

A solid proof is when the proof has absolute mathematical background..thats all..

Answer 15

Alright then before I go, what was your approach or goal to trying to prove it?

Answer 16

Thats a hard thing to say...ur proofs were quite simple for me...but proofs that I need to do in my classes are hard enough..and the approach comes through practice I believe..U have to see through the problem and guess how u could manipulate the statement to be proved mathematically to prove it

Answer 17

Well once you know how to go about them then Im sure they are simple. I just wasnt sure if you had a specific goal thatyou were after.

Answer 18

There's one goal..enjoy proving it...and don't get bored in the middle

Answer 19

Haha, alright then. Sorry for taking your time xD

Answer 20

oh c'mon...I'm having free tym now...

Answer 21

xDD well much appreciated then :3

Answer 22

:)..I hate formal statements...they mke me feel lyk pellet..:P