Mathematicians Discovered a Computer Problem that No One Can Ever Solve

livescience.com ^ | January 11, 2019 08:08am ET | By Rafi Letzter,

[Joe Bfstplk]

They need all the numbers they can find to state our national indebtedness.

[BEJ]

A lot of good answers here. I think “infinity” is an invention of the mind. If there was a true infinity, an infinity with anything physical that has volume, we wouldn’t exist, because we would limit infinity by our presence. In other words, we are taking up space where what we are measuring should exist in, which means that infinity is lacking. Infinity is less and, therefore, not infinite. It’s the same with God. To say that God exists infinitely everywhere, then there is no space or room for us.

[zeugma]

Interesting. I really with that when I was younger someone had pointed out to me some of the weird things that can happen with math. Things like Collatz systems and the like. It might have made me more interested in it.

[zeugma]

And in February, 2002, at a Department of Defense briefing, Donald Rumsfeld agreed:

"There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know."

That wasn't original to him. I never understood the crap he took for making the statement. It's absolutely true. It's the unknown unknowns that really bite you in the ass.

[zeugma]

I have a proof for this, but there’s insufficient space to show it here.

What you did there. We saw it.

[IronJack]

Integers are countably infinite

"Countably infinite" is a contradiction in terms. If it's countable, it's not infinite. By definition.

That reals are different than integers does not make either of them countable, or one of a "greater" infinity than the other.

Infinity is not a number. Thus, no arithmetic comparators apply to it. Terms like "greater" or "lesser," "more" or "fewer" are meaningless.

[spokeshave2]

It has been solved. The answer is, of course, 42.

And is the rounded number from 41.7

[chickenlips]

WOW! This sounds even to big for even AOC to solve!

[spokeshave2]

For all practical purposes, the answer is “No.” Or is it?

Dr. Edward de Bono invented the word PO as intermediate between YES and NO

I think in Japanese its HA

[spokeshave2]

For all practical purposes, the answer is “No.” Or is it?

Dr. Edward de Bono invented the word PO as intermediate between YES and NO

I think in Japanese its HA

[BenLurkin]

Ping

[Hegemony Cricket]

Bump for later

[so_real]

"But even though there are infinitely many integers and infinitely many real numbers, there are clearly more real numbers than there are integers."

Fail. This statement attaches "magic" to the decimal point. The decimal point is arbitrary. Without it there is only an infinite series of integers. If we had brains capable of understanding the true smallest possible undivided unit, and perform maths at levels infinitely larger than this, we would not require decimal places at all. Only because of the limited observational and computational power of mankind are decimals used.

[itsahoot]

OTOH, there are infinity-deniers:

I wrote out an infinite string of numbers once but I showed it to my wife and she added one and messed it up.

[itsahoot]

That's not without getting into Complex Numbers

Not to mention the imaginary ones.

[Susquehanna Patriot]

You are a very lucky man to have such balance in your life, and to help with spelling too!

[coloradan]

You are mistaken. There are infinitely many integers, because, for any integer, one can always obtain a larger one. However, they are countable in that they can be ordered, giving each one a place, with a definite “next one” and a definite “previous one” - in the case of every single integer.

In particular, for any given integer, there is always a “next one” and so the set of integers is infinite. (Indeed, even the set of “positive integers” is infinite.)

Just because something is countable doesn’t mean it isn’t infinite. In order to be not infinite, there has to be a finite number of them - a last one of them. The number of ways a deck of cards can be ordered is finite. It’s a huge number, but, it is a definite number, and there are no other ways the deck can be ordered other than as one of those ways. But there is no last integer; one can always get a larger integer by taking the factorial, by squaring it, or even, modestly, by just adding 1.

[right way right]

The answer could be anything.
More research money is needed.

[IronJack]

I think I understand the distinction. It seems a little bit like semantic hair-splitting, but I’ll concede the point.

[GingisK]

Throw in floating point, and nothing is truly accurate.

Stephen Hawking said, "God created the integers. Floating point belongs to Satan".