Is this sentence correct ?

[emsr2d2]

That's OK, but how could you both leave out "in" from "a better place to live in"? Do you really both prefer, "The world would be a better place to live if ..."?

I do, yes.

England is a great place to live.
The block of flats on the east side of town is a terrible place to live.
This world is a fantastic place to live.

With none of those, would I say "live in" so I wouldn't use it in the OP's sentence either.

I live in London. It's a great place to live.
Would you say "I live in London. It's a great place to live in"?

[Raymott]

I do, yes.

England is a great place to live. Is that why you live it? I might use "in" here.
The block of flats on the east side of town is a terrible place to live. People generally live in a block of flats. I don't see an objection to "in" here, though I might leave it out.
This world is a fantastic place to live. in.

With none of those, would I say "live in" so I wouldn't use it in the OP's sentence either.

I live in London. It's a great place to live.
Would you say "I live in London. It's a great place to live in"? Probably 50/50.
If I actually lived in London, I might not, because I'd talk like other Londoners, who apparently don't use "in" here.
But I'd say, "Brisbane is a great place to live in."

Would you say, "What's London like to live?"
Would you say, "London is a great place to live. That's why I live it."?

But I would say, "The world could be a better place to live in." I was just surprised that both you and bhai chose the form without "in"
But it's no big deal.

[emsr2d2]

BrE vs AusE difference, perhaps.