I think the last one is the type im looking for, could someone show me how that might work with a number like

209383404?

Thanks

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- Jan 5th 2010, 09:33 PMhebby
I think the last one is the type im looking for, could someone show me how that might work with a number like

209383404?

Thanks - Jan 6th 2010, 03:31 AMHallsofIvy
You have been given two equivalent expressions.

$\displaystyle \lfloor x\rfloor$, called the "floor" or "integer part" (for positive numbers) gives the largest integer larger than or equal to x.

$\displaystyle \{x\}$, called the "decimal part" is $\displaystyle x-\lfloor{x}\rfloor$.

If x= 209383404, then x/1000= 209383.404. It's "floor" is 209383.

Or if x= 209383404, x/1000= 209383.404. It's "decimal part" is .404 and then 209383.404- .404= 209383. - Jan 6th 2010, 07:55 AMBingk
Hi ... Yeah, I know that it's essentially the same, but it goes back to my question about the floor function being an operation (i.e. I'm pretty sure it is also an operation, but I'm wondering if there's any significance in it being called a function rather than an operation)

Also, I asked if my proposal was okay, because I think it fails the requirement of two operations ...

hebby, this is how it would work:

$\displaystyle 404 \equiv 209383404 \ mod \ 1000$

So,

$\displaystyle \frac{209383404 - 404}{1000} = 209383$ - Jan 6th 2010, 08:07 AMDrexel28
- Jan 6th 2010, 02:01 PMBingk
Hi ... I actually had a response typed out before I lost electricity (and thus internet connection) ...

That's kind of my point, why is it called an operation instead of a function? Why floor function instead of floor operation? Similarly, why addition operation, instead of addition function? Is there any particular reason for this terminology? I know the main difference between an operation and a function is that an operation maps to only one "dimension", whilst functions can be mapped to more.

In any case, this is kinda heading off-topic ...

hebby, depending on how much calculus you've learnt, you should be familiar with the floor function, and I think that would be the solution. Otherwise, well ... you'll have to think of something :) - Jan 6th 2010, 02:34 PMDrexel28
- Jan 9th 2010, 10:13 PMBingk
Um, there's something wrong with your latex, but I'm guessing you're saying that f:R^2 -> R^2 ... and yeah, that is a function, and I did say that functions can be mapped to more than one dimension. It's operations that are limited to R^n -> R.

I was just wondering (since my math is limited), why the distinction between operation and function, and why in particular some functions are distinguished as operations, whilst others are not (even though they are also operations) ... such as the floor function ....

:) - Jan 9th 2010, 10:41 PMBacterius
An operation is a very basic calculation based on an axiom : addition, multiplication, division, modulus, substraction, etc ... They can be used on their own or as parts of functions to accomplish something. Example : $\displaystyle 4 + 4$, $\displaystyle 3 \times 9$, $\displaystyle 7 \equiv 3 \pmod{4}$ ... An operation can be viewed as a simple function.

A function is a combination of operations arranged in order to achieve a particular goal. Take the factorial as an example : $\displaystyle n! = 2 \times 3 \times 4 \times ... \times n$. This is a combination of $\displaystyle n - 1$ multiplications, arranged in order to obtain the factorial of a number.

A function is not necessarily defined as $\displaystyle f(x)$ or $\displaystyle g(x, y)$ or any other letter. $\displaystyle n!$ is a function. $\displaystyle \sqrt{x}$ is a function. $\displaystyle e^x$ is a function. Etc ...

Do you understand better now ? - Jan 9th 2010, 10:55 PMBingk
yup ... makes more sense ... but if that is the case, going back to hebby's original question, then I don't think we could use the floor function ....

For your convenience ... hebby is asking how you can "cut off" the last three digits (on the right), of some integer, in two mathematical operations ...

i.e. 123456 becomes 123 - Jan 9th 2010, 11:10 PMBacterius
I don't know if this is possible in two operations. I can do it in three, but I can't find a way to do it in two. Anyway, what is the point of this kind of question ? If one can find a way to do it somehow, one will do it this way until further improvement, don't you think ? He won't just be looking for something that takes two operations ...

- Jan 10th 2010, 12:19 PMDrexel28
- Jan 10th 2010, 12:19 PMDrexel28
- Jan 10th 2010, 01:52 PMCaptainBlack
- Jan 11th 2010, 02:23 PMBingk
Hi, just wondering, would this be considered an operation then: $\displaystyle f:\mathbb{R}\times\mathbb{R}\mapsto\mathbb{R}^2$ given by $\displaystyle f\left(x,y\right)=\left(x,y\right)$?

Cuz from what you gave, I can still see how it's kind of "one dimensional" (the only dimension is $\displaystyle R^2$)

Since you disagree with Bacterius, how would you distinguish operations from functions? Just curious as to how different people's views are :) - Jan 11th 2010, 02:36 PMDrexel28