Math Is Fun Forum

I learnt a bit of assembly - if you're learning just to do things quickly though, it'll be a struggle. Now-a-days you'll have to be a very good assembly programmer if you want to beat a modern C-compiler that optimises well. Also, the maths coprocessor is out-dated, going back to the times when it was a kind of "add-on" that allowed programmers to make faster programs, but only if you had the coprocessor. Today all the functions of a coprocessor are built into the CPU.

To be fair George, you have been guilty of this yourself. And sometimes you don't make a whole lot of sense. Also, what has your "apples" example got to do with anything? Could you please tell all how it is relevant?

How can there be an infinite amount of digits after the decimal place and they aren't endless (i.e. have no end) - these two are mutually exclusive. Have one, fine - have the other, great - but you can't have them both simply by their very nature.

Two prisoners, one polish and one british, escape from prison. After traveling on foot for four days they come to an airport, the british man luckily knowing how to fly. Barging on-board a nearby aircraft they manage to get everyone else off, but in the struggle the brit is hurt so badly it would be impossible for him to pilot the thing. Instead, the polish man sits at the controls and - though he has no flying experience - the brit talks him through what to do.

Still on the ground, they hear sirens in the distance. As the sirens get louder and louder the brit starts to panic and begins barking orders at the polish man, who is having difficulty getting everything in order.

"Push that button there!"
"Where?"
"The one I told you about earlier!"
"Which one?"
"THERE! Left, left, down, UP! COME ON MAN, THERE'S NOT MUCH TIME!"

Eventually, the two are captured, the aircraft having never moved. As the two are led away, the brit shouts out:

"Why couldn't you fly the darn aircraft - I told you how!"

The response comes:

"Ah, but I was only a simple pole in a complex plane!"

There are 3 types of people in this world: those who are good at maths and those that aren't.

An enginer, a physicist and a mathematician are watching a building they are sure is empty. They see one person come in, and then two come out a while later.
The engineer thinks: We can't tell if the building is empty, as more may have got in through a door we obviously don't know about.
The physicist thinks: Ah, now the building is empty.
The mathematician thinks: If one more person goes into the building it'll be empty again.

A student tries to dial a disconnected number from a phone within the university mathematics department. He gets the message:
"Sorry, the number you have dialed is imaginary. Please rotate your phone pi over two radians and try again."

I second what Mathsy said - as has already been stated, just because the series is infinitely long does not mean it "grows" over time. 0.9999... has exactly the same number of digits at this moment in time as it does in any other moment in time.

Also, your post is quite vague - could you please highlight exactly what you are unhappy with about the way base-3 arithmemtic (or any other arithmetic) is used in my last post? If you can't, there must be nothing wrong with it, and it must be correct.

What Luca said. For the number 0.1111..., for every natural number n you give me, I can tell you what digit is at that position, and that digit will always be one. However, there is no natural number that you can give me such that the nth digit of 0.0000...0001* is equal to 1. Thus this number* is equal to 0. Happy with that?
If you want to say that 0.0000... has the same number of digits as 0.1111..., that's fine, I'll agree with you. So long as you recognise that 0.0000...0001 doesn't actually make sense (or at least that it's equivalent to 0).

Right - I think what you're trying to do is ask me what the second to last digit is - there is no such digit because there is not a last digit. The string of digits never terminates. Note that this does not mean that the number is "non-static" or changing or anything like that, it just means that trying to find the last digit is like trying to find the largest integer - you can't do it. Not because you're not good enough, but because there isn't one.

* Assuming for a second that this number even makes sense.

0.1111... does not "change value" over time. For example, the value of 0.13 is always the same - it doesn't "start" at 0 and then "become" 0.1 and then "become" 0.13. Numbers do not change with time. 0.1111... always has the same value, and it has an infinite number of digits after the decimal place - what's the problem with this?

Also, what exactly are "finiteth" and "infiniteth" supposed to mean? Please don't make up words.

From the bold text, it is then clear that "the Infinite Difference!" = 0.1, which is clearly wrong.

But there are an infinite amound of digits in it. That's what the dots at the end indicate. 0.1111... means that the "1"-digits repeat endlessly - i.e. there are an infinite amount of them.

What do you mean "have I gotten"? (assume by "any finiteth digit" you mean "any digit", right?)

Do you mean to ask if I, personally, have written down on some piece of paper the number that includes every digit of 0.1111...?