Flowers for Algertron.

I should have been clearer. I was hoping to get the point across that "math isn't just for mathematicians". Anyone can try these ideas out.

Obviously, I failed at clear communication. However, you failed at reading comprehension.

See ShayGuy's explanation of mathematical induction above.

This is just an algorithm, and there are many algorithms that provably halt on any input.

I'm not sure what number you really started with, but if it was 692494933391927319282416798693, then it arrives at 1 after 698 Collatz iterations.

It's pretty easy to do this in most programming languages. In Mathematica, you might do this:

Excellent free Facebook status.

It's because people seem to think, intuitively, that decimal notions must somehow uniquely identify real numbers. I don't think anyone is born with a notion of decimals, so this misconception probably has its origin in elementary school math instruction.

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What do you mean by "equal"?

My daughter loves this song, but not quite as much as "Birdhouse in Your Soul".

The most obvious reason, to me, is testing current models of the nucleus and nuclear theory. The models predict which nuclei should be stable, which should decay, and particularly how long they last on average and the decay process. Classify this reason as "science".

I'm posting to your reply to clarify my opinion rather than post to both triggerx and Copperbottoms. I think you see my point.

"Now, what had happened in those, I couldn't tell whether the bullet went through the ear and out the eye cavity or through the eye and out the ear because a lot of brains were draped out from the socket."

1. Linear time reductions are useful but not in this context. The appropriate reduction is a polytime reduction because the class P is closed under them. If I apply a polynomial time algorithm to another polynomial time algorithm, I still have a polynomial time algorithm. So I know that if I can reduce some…

Yes, if you do the reduction as you describe, then a polynomial time computation on a quantum computer would take exponential time. However, it has not been proved that this is the best anyone can do. For example, I could compute the product of two integers on a quantum computer, which I can do in Omega(n). If I…

That is to say, a quantum computer can easily simulate a Universal Computer (any universal computer), but a Universal Computer can't simulate a quantum computer.

Thanks. I'm happy someone else found them interesting.

Ok, the study is behind a paywall (again, grrr....), but the checklist is available: