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January 21[edit]

Use of prime numbers[edit]

Plese mention the uses of Prime numbers with examples Kasiraoj (talk) 01:54, 21 January 2012 (UTC)[reply]

Per WP:WHAAOE, Prime_numbers#Applications is a good place to start. --Kinu ^t/_c 02:14, 21 January 2012 (UTC)[reply]

And (mentioned elsewhere in the article but not under applications) there is always the application of using them to identify alien transmissions. That is, a prime number sequence is considered to be extremely unlikely to be generated without intelligence, so any prime number sequence we receive from outer space makes it quite likely that it was sent by aliens. Conversely, if we send out a prime number sequence, that should identify us as "intelligent" to any aliens who receive the message. StuRat (talk) 20:55, 21 January 2012 (UTC)[reply]

She can't be right, surely[edit]

Hi. I'm trying to convince my (secondary school, UK) Maths teacher that -0 is an actual number. In my head, thinking of limits, I feel it makes sense, and know what I want to convey, but her counter-arguments always leave me floundering. Many thanks81.155.242.161 (talk) 20:07, 21 January 2012 (UTC)[reply]

Take a look at Signed zero. Qwfp (talk) 20:37, 21 January 2012 (UTC)[reply]

Though it should be stressed that if by "number" we mean "real" or "complex" number,

+0=-0

. Why do you believe that they are distinct? What is the crux of your confusion?--Leon (talk) 20:40, 21 January 2012 (UTC)[reply]

It is an actual number, but unless you have assigned it notational meaning, −0=+0. In my experience, −0 can exist for engineering reasons (a sign bit) or as a notational shorthand for one-sided limits, which is fine with some prose to let your reader know that when you say

f(-0)\neq f(+0)

you actually mean

\lim _{x\to 0^{+}}f(x)\neq \lim _{x\to 0^{-}}f(x)

.

But in general, without any introduction, −0=+0. So you aren't wrong to have the feeling that −0 should have a distinct meaning, but it's not exactly correct to say it's a separate number from zero unless you are using it as (perfectly valid) notational shorthand. (Note that other numbers have more than one representation. For example, 0.999… = 1.) —Ben FrantzDale (talk) 21:07, 21 January 2012 (UTC)[reply]

The problem is purely a matter of definition. What do you mean when you say "an actual number"? There are many ways that the terminology can be used. I use computers to do most of my math, so my example shows the way many computer programmers explicitly define mathematical terminology.

Most modern computers use the IEEE-754 standard representation for floating point numbers. In this system, +0 and -0 are distinct entities. Most modern computers also allow us to use integer representations of numbers, for which there is no distinction between positive and negative zero in the data primitive type. If we are speaking to computers, we use a programming language that allows us to make such distinctions abundantly clear:

Sample C Program to explicitly define several types of zeros

#include <stdio.h>
int main() 
{
signed int zero0  = 0 ;
signed int zero1  = -(1.0 * 0.0) ;
double     zero2  = 0.0 ;
double     zero3  = -(1.0 * 0.0) ;
char       zero4  = '\0' ; 

fprintf(stdout, " %d, %d;    %lf, %lf;  %c !!\n", zero0, zero1, zero2, zero3, zero4)  ;

return 0;
}

There sure are a lot of zeros in my sample code, which correctly compiled and printed

0, 0; 0.000000, -0.000000; !!

...on my system. (Some people who compile this code will not see the trailing exclamation points on their computer systems!) The most important detail is that the exact same program code, "-(1.0 * 0.0)", produced a different result, based on how I defined my numbers.

In normal English parlance, we don't always use such precise terminology to distinguish between number types; but if you're planning a pedantic debate over what counts as an "actual number," you should be prepared to define what that means. Nimur (talk) 21:10, 21 January 2012 (UTC)[reply]

Usually in math class by "number" we mean standard reals or integers, not computer arithmetic (e.g. IEEE-754 arithmetic is non-associative). In this usual sense, -0 and +0 are both actual numbers and in fact they're both the same number, just like 2+2 and 3+1 are the same number. 67.122.210.96 (talk) 22:26, 21 January 2012 (UTC)[reply]

Meteorologists use −0 when tabulating temperature listings that have been rounded to the nearest integer, for example, to determine when the temperature drops below freezing. For example, if the temperature is +0.3 °C, it will be rounded to +0 °C, which is above freezing; if it is −0.3 °C (below freezing), it will be recorded as −0 °C. The distinction can be significant in weather tracking. — Michael J 00:39, 24 January 2012 (UTC)[reply]

In a group it is trivial that the opposite of the neutral element is the element itself. Thus, in the additive group of real numbers the symmetric of zero is zero itself, therefore a number. You see, in algebra -0 means nothing more than "the symmetric of 0". On the other hand, you say you think of limits. That is, you approach 0 coming from below, through greater and greater negative real numbers yet never reaching 0, and you feel you have a number there: a number greater than any negative number and at the same time less than 0. Well, that does not exist in the real number set. That's why the infinitesimals were invented. As far as I know Leibniz was the first person who tried to formalise the idea. Unsuccessfully. I think Archimedes also thought in terms of infinitesimals. Sometimes, at least. It was modern Non-standard analysis that founded the concept in formal terms. In this non-standard analysis, there are such amounts greater than 0 yet less than any positive real number - the infinitely little ones, and amounts greater than any positive real number - the infinitely great ones. Which people sum and divide as any other number, performing that way all of Classical analysis with simple algebra. Garsd (talk) 22:57, 25 January 2012 (UTC)[reply]