View Full Version : Why does No mean what we think it does?

SilsoeSid

10th May 2005, 20:16

Sitting waiting for the family pub lunch to arrive. I am asked one of those questions that only children ask !!

On reading the instructions on how to order your meal, little Miss Sid asks, "Dad, whats a table No?"

"That is short for table number", says I.

"But there is no 'o' in number dad!" She replies.

"Well done" I hastily reply, knowing full well what is coming next. Before I can change the subject....

"So why is it 'No' and not 'Nu' Dad?

"That's a very good question and it's just one of those things about the English language that makes it so special."

"Yea Dad, but Why?"

"I don't know, but we can find out later..."

.....Help!!

Onan the Clumsy

10th May 2005, 20:23

Numero

Solid Rust Twotter

10th May 2005, 20:27

Nombre?

...And a filler for bandwidth utilisation purposes.....

Onan the Clumsy

10th May 2005, 20:34

I didn't need a filler

Nah nah nah nah naaaaaaah

:8

rustle

10th May 2005, 20:39

Somone once asked the definition of "number" and got this:

Number: The concept of number is the most basic and fundamental in the world of science and mathematics. Yet a satisfactory answer was attained only in 1884 A.D. by Fregé [2], the founder of modern mathematical logic. His answer remained unknown to the world until Bertrand Russell, the English mathematician and logician, in his attempt to base all of mathematics in terms of the concept of sets, rediscovered the concept of number.

The concept of number is associated with the concept of a "set." By a set is meant a collection of definite and separate objects for which we can decide whether or not a given object belongs. So to exhibit a set, you show all the objects - popularly called elements - in the collection by either exhibiting each individual element in the collection or precisely describing which elements belong. An instance of the former is the set {Bob, Mary and Marg}; the set is exhibited by providing a list of its elements inside two curly brackets. In showing a set by describing its members, rather than exhibiting the individual members, we can use ordinary language when that will do - for example, the set of all people on earth. Or, we can also use curly brackets thus: {x | x is a person of the Earth}; where the vertical line means "satisfying the condition that," or simply "such that."

Equivalent Sets

Let A be the name of the set comprised of Bob, Mary and Marg. Let B be the set {Brian, chair, Mississippi river} . Consider a correspondence between A and B:

Bob --> chair

Mary --> Brian

Marg --> Mississippi river

In fact, we can write down five more such correspondences! Let us use the one above. Such a correspondence is called a one-to-one (often written 1-1) correspondence from A on to (often written "onto")B. A member of each set is accounted for exactly once in a 1-1 onto correspondence. A 1-1 onto correspondence from A to B has the property that you can reverse the arrows and get a 1-1 onto correspondence from B to A.

It is not always easy to show that a correspondence is onto, especially when dealing with infinite sets. But if we can show a 1-1 correspondence from set A to set B and another 1-1 correspondence from B to A, then there exists a correspondence from A to B that is 1-1 and onto; this is the Schröder-Bernstein Theorem.

Mathematicians call a 1-1 onto correspondence also a "bijection." They say A is "bijective" with B. This is really a fancy way of saying that there is a way of matching up the elements of A with those in B so that each object in A corresponds to exactly one object in B, and vice versa. Now, there are all kinds of sets that are bijective with A. So we might as well continue with A and B. The sets A and B share a quality. That quality is called the "cardinal" number. Cardinal means important. The cardinal number of our A or B is written as "3". We will call this important number just "number."

So what is a number? It is that property of sets which is common to all sets that are bijective with each other. Two sets that are bijective with each other are also called "equivalent" sets. So our A and B are equivalent sets. A number is the property common to equivalent sets.

Numeral

Numeral is the symbol for the idea called number. Put another way, the number is the idea we think of when we see the numeral or when we see or hear the word for a numeral.

Suppose there is a person named Jim. This person has the name Jim because he was named so. It is very convenient! A numeral is like the name Jim.

Now, if someone says number 3, we know what really is meant. 3 is the numeral for the number the person wishes to communicate to us. Since this is to be always understood, we just say "number 3."

An alien coming to earth might be amused to note that we have given this number the name 3. A computer on earth would have to be told that this number is 11, because 11 is 3 in binary notation. 11 in binary and 3 in decimal notation are called "numerals." As you know, III is the Roman numeral for 3. These are all names for the quality shared by all sets that are bijective with the set A above. Or the set B above!

On the web page "Numeration systems," we discuss the various systems like the binary, decimal and others for writing numerals.

Cardinal Numbers and Ordinal Numbers

There are mainly two kinds of numbers: cardinals and ordinals. Cardinal numbers tell how many things there are in a set, as in "There are four people in my family." If you consider a set and a copy of it, you get two identical sets which are clearly equivalent. The number here is often referred to as the "cardinality" of the set; it is still the cardinal number of the set. The cardinality of a set is the size of the set; it is the number of things - or elements - in the set.

Ordinal numbers have to do with the order or priority of the elements in a set that has such order or priority for all its elements. So ordinal numbers give the positions of elements in an ordered set. For example, "I am fourth in the queue for lunch." The word "fourth" denotes an ordinal number.

Zero

0 is the quality shared by all sets that contain nothing. Mathematicians call such sets, the empty sets. So 0 is not nothing; it is a numeral or let us be lazy like everybody else and call it a number! So if you are asked if zero is a number, you could say "well, it is." "Well" because it is a number in the sense of being a numeral. Well, it should be really called a numeral. But number will do.

Since that was all a bit of a mouthful, they decided to abbreviate it somewhat and selected the first and last letters only - hence "No."

HTH ;)

PS I didn't need a filler either :=

Solid Rust Twotter

10th May 2005, 20:40

Moderator's pet...!

Nah, nah nah nah, nah........

Sulks...

Onan the Clumsy

10th May 2005, 20:49

Since that was all a bit of a mouthful, they decided to abbreviate it somewhat and selected the first and last letters only - hence "No." Is taht porof taht you olny need to raed the frist and lsat ltertes to udnretsnad smeohitng?

scrubed

10th May 2005, 21:20

Oh conch rare.

I hear "No" all the time and generally find it eventually means "Yes" if I apply myself a little...

XXTSGR

11th May 2005, 01:30

We tend to use the hash symbol - # to mean "number".

But why on earth do the Americans call it the "pound" symbol? The pound symbol is £. Isn't it...? :confused:

BahrainLad

11th May 2005, 02:18

"I don't know, but we can find out later..."

Should've given them a head-start against their peers and said "Well kids, there's a wonderful tool called Google that we can ask when we get home...."

GrumpyOldFart

11th May 2005, 04:56

But why on earth do the Americans call it the "pound" symbol? The pound symbol is £. Isn't it...?

Yes, but they pronounce it lb. (Rhymes with 'pub' in Yorkshirese)

Avtrician

11th May 2005, 05:45

I had to wonder about the Yanks and # (pound key) when I was using some fax software. It was saying that if you wanted to leave a message then use the pound key. Every one knows there is no pound key on a phone.!!!!!

(dont have one on this key board either and dont know how to get it from the other character set.):bored: :bored: :hmm:

In hospitals the # symbol means fracture. Now being a phone tech I was quite concerned when I heard someone say they were going to fracture the phone. What they actually meant was they were going to forward the phone. It was the feature codes for forwarding that started with # and so the term was adopted.

And to think I once thought # was hash - hence #ish or preparation for naughts and crosses.

OK then how did this thing ~ get to be called a tilde or even circa - or is it just something else?

Kalium Chloride

11th May 2005, 09:27

From 'Mathworld':

To indicate a particular numerical label, the abbreviation "no." is sometimes used (deriving from "numero," the ablative case of the Latin "numerus"), as is the less common "nr." The symbol # (known as the octothorpe) is commonly used to denote "number."

Heatseeker

11th May 2005, 11:59

Wot a clever lot you all are.

Anybody got the numero's for this week's lottery ? Anything else would just be hash.

Heat

tony draper

11th May 2005, 12:15

In the building trade the hash symbol on a wall means someone has been playing noughts and crosses.

:cool:

Tuba Mirum

11th May 2005, 12:21

OK then how did this thing ~ get to be called a tilde or even circa - or is it just something else?

"Tilde" is a Spanish word from the Latin "titulus", meaning "title", or "label".

This seems to be descriptive more of what it looks like than of its actual role, which in Spanish is to turn a "ner" sound into a "nyer" sound, and in Portuguese to "nasalize" a vowel. I haven't come across it in any other circumstances.

Heatseeker

11th May 2005, 12:32

I've got a nyer thingy on my keyboard but whenever I press it all I ever hear is f:mad: k

H

tall and tasty

11th May 2005, 12:35

The joys of being a parent and to think they can bombared us with anything up to 400 of this why questions every day!

My mother always told us to refer to the encyclopedia so we remembered what we looked up!

But how do you look up "Why are there no bull dogs in Africa?????"

TnT

:p

acbus1

11th May 2005, 17:08

Sometimes all the keys on my keyboard are pound keys......... :mad:

Onan the Clumsy

11th May 2005, 17:28

how did this thing ~ get to be ... circa Perhaps because two of them on top of each other means "approximately equal to". Keyboards don't have that symbol, but this is a good substitute.

I thought the Octothorpe specifically refered to the pound sign on the telephone keypad.

I read a web page once written by the guy who "invented" the symbol. Can't remember though if he was called Mr. Octo or Mr. Thorpe.

XXTSGR

11th May 2005, 19:10

"Octothorpe"?? Why? Because it has ~four strokes? Or because it has ~nine cells? :E :uhoh: :rolleyes: :confused:

Tuba Mirum

11th May 2005, 22:29

:\

(padded out for length, but still just means "Whoops!")

Blacksheep

12th May 2005, 05:28

I reckon he was called Don Macpherson (http://www.sigtel.com/tel_tech_octothorpe.html), Onan