# Why does No mean what we think it does?

Purveyor of Egg Liqueur to Lucifer

Thread Starter

Join Date: Nov 2002

Location: Alles über die platz

Posts: 4,615

**Why does No mean what we think it does?**

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!!

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!!

Join Date: Aug 2002

Location: Surrey, UK.

Posts: 1,314

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

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

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.

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.

HTH

PS I didn't need a filler either

I'matightbastard

Join Date: Jul 2001

Location: Texas

Posts: 1,746

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."

Chief Tardis Technician

Join Date: Jan 2001

Location: Western Australia S31.715 E115.737

Age: 66

Posts: 554

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.)

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

ανώνυμος

Join Date: Feb 2004

Location: Perth

Posts: 111

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.

Join Date: Nov 1999

Location: South East UK

Posts: 428

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."

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."

Guest

Posts: n/a

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

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.