Simple but as yet unsolvable math problem

[Brad Johnson]

Interesting, but now my brain hurts.

The Collatz Conjecture. A simple equation that mathematicians have spent decades trying to untangle

https://www.youtube.com/watch?v=094y1Z2wpJg

Brad

[K Frame]

Not going to watch it.

I have enough trouble with 2x2.

And don't you know that mathematics is racist/sexist/somethingist because it demands, and arrives at, concrete answers?

[just Warren]

Of course it's unprovable.

Numbers are infinite, you'd have to check each one. And that's not possible.

However just by using common sense I can tell you it's true.

That's because if you've checked so many numbers now and it's never failed it's not going to fail.

There's nothing special about the next higher number that will render it untrue.

If the number is even you will go back to a number you've already checked.

If the number is odd you will land on a new number but it will be even and when halved and higher than your starting point but if it is even it will be halved and then you will be at a number you've already checked.

If the number is odd and is 3*+1 that makes it even again and will be halved and if you're using a computer you've been checking numbers in sequence and will have gotten to that number to check it. And if even it will land on a number you checked many cycles ago.

In the event that the odd number is so large that halving it does not quickly get you to a number you've checked, just give it a while and it will.

This process has already played out with smaller numbers so what will change with larger numbers?

Is there any combination of 0-9 in smaller numbers of, say, 5,6,7,8,9 digit that has yet proven untrue? No? Then why would we expect that to change just because the number of digits increases to 10,11,12 and so on?

[just Warren]

And what is the point?

What if, somehow it was found to be untrue?

Does that upend all of math?

Does that mean 2+2 is invalidated?

Algebra?

Geometry?

Calculus?

Will we not be able to put rockets in space or count our change after a purchase?

Will find the area of something now become impossible?

Will the Count from Sesame Street be declared obsolete and suffer the fate of the Burgess Meredith character in that one Twilight Zone episode?

[Brad Johnson]

Have you considered switching to decaf?

Brad

[K Frame]

Or a Snickers...

[ConstitutionCowboy]

We hold these truths to be self evident. 

Woody

[Fly320s]

I'm with Warren.  "Solving" this problem is just a game for nerds.

It isn't even a problem.  It is a, "Huh.  That is kind of neat."

[230RN]

Were I inclined to "use up" (euphemism for "waste") time on this problem, I'd look again at how you prove that operations which result in irrational numbers really do.

Take pi, for example, or any of the irrational constants.

In the case of 2 ÷ 3, it can be seen that the next digit "down' will always be 6, and no need to explore that down to the billionth iteration.

I would say the "proof"  is that every time we choose a number, the operation yields the same result.  Not "rigorous," but good enough for me.  Sort of like empirically-derived engineering solutions.

One thing I wonder about, without trying it, is to see what happens if we perform analogous operations on different numbering systems (radices) such as hexadecimal or (egad!) binary.

I certainly understand the desire to develop a rigorous proof of the assertion.

But I'm old enough to not wish to budget more time on it.

As I tell folks, the older you get, the more practical you get.

Terry, 230RN

[ConstitutionCowboy]

In the case of 2 ÷ 3, it can be seen that the next digit "down' will always be 6, and no need to explore that down to the billionth iteration.

It's why we can't go without fractions. Ya gotta have both.

Woody

[230RN]

All you're doing with fractions is selecting a denominator which would most closely match the last decimal digit you calculated.

Pi is 3   1 4 1 5 9 2 /100,000 ths

or,

3    1 4 1 5 9 2 6 5 /10,000,000 ths

But that still isn't

3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3

Now, I think at one point Louisiana passed a law that 22/7 would be used in all calculations which used pi, which isn't off by much.  The error in calculating the circumference of the earth is only about 10 miles if my arithmetic is correct.

[Jim147]

The answer is 2. I'm done. I didn't even click on the link.

[WLJ]

42

[just Warren]

42

42/2 = 21*3=63+1=64/2=32/2=16/2=8/2=4/2=2/2=1

True.