What is this symbol? ordered field

In summary, the conversation discusses the representation of an ordered field in mathematical notation, specifically the use of different symbols and typefaces such as F, H, and \mathbb{F}. The conversation also touches on the use of different notations for finite fields and the humorous misunderstanding of the word "field" in mathematics.
  • #1
flyingpig
2,579
1
It looks like an F, but it also has an e

[PLAIN]http://img98.imageshack.us/img98/2161/unledbto.jpg [Broken]

It means like ordered field

Thanks
 
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  • #2
Could it be a script F?

[PLAIN]http://www.decodeunicode.org/en/data/glyph/196x196/2131.gif [Broken]
 
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  • #3
There is no e in yours and it looks like yours is bolded
 
  • #4
I thought that perhaps the e might actually be the kind of loop you see on my F.

Sorry that it is bolded. :blushing: It was just the first F I could find that had such a loop.As an alternative it might be a H...

[PLAIN]http://typophile.com/files/H_6027.gif [Broken]

or

[URL]http://images.inmagine.com/img/valueclips/unc269/u26688036.jpg[/URL]

I found one with flowers! :biggrin:
 
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  • #5
OKay but what is it called?
 
  • #6
flyingpig said:
OKay but what is it called?

H, pronounced "aych":biggrin:
In what context does it appear? Preferably, post the expression.
 
  • #7
I tried [tex]\aych[/tex]

Nothing

It appears in Ordered Field
 
  • #8
flyingpig said:
OKay but what is it called?

Since it is supposed to represent an (ordered) field, I think F, pronounced "ef", which is the first letter of "field".
 
  • #9
[tex]\ef[/tex]

[tex]\ofield[/tex]

None of them are working
 
  • #10
Unless it is an H, in which case mayhaps it refers to the quaternions? (it would be a strange font, though...)

None of them are working

It's just a stylized letter, it can mean whatever you want. It isn't going to be under "/field" or anything like that.
 
  • #11
flyingpig said:
I tried [tex]\aych[/tex]

Nothing

It appears in Ordered Field

appears...where?
 
  • #12
Math, Ordered Field, it appears in
 
  • #13
flyingpig said:
Math, Ordered Field, it appears in

Quote the passage in which it appears.
 
  • #14
It seems you're trying Latex?

That would be:
[tex]\mathscr F[/tex]
or
[tex]\mathcal F[/tex]
 
  • #15
it kinda looks like it, but is it correct to use it?
 
  • #16
flyingpig said:
it kinda looks like it, but is it correct to use it?

Hmm, this may seem a bit repetitive, but I have to ask... use it when and where? :confused:
 
  • #17
Oh, and as for the name, perhaps the Unicode name "SCRIPT CAPITAL F" (code U02131) covers it?
 
  • #18
for ordered fields.
 
  • #19
flyingpig said:
for ordered fields.

Yes, you can use script capital F for an ordered field.
 
  • #20
what about [tex]\mathbb{F}[/tex]? is that just for normal fields and not ordered ones?
 
  • #21
flyingpig said:
what about [tex]\mathbb{F}[/tex]? is that just for normal fields and not ordered ones?

I'm not aware of any convention for the typography to represent a field.
This means you can use any typeface you want.
Most common seems to be simply italic F ([itex]F[/itex]).

Also, there's no distinction in typography for an ordered field.
 
  • #22
The notation [itex]\mathbb{F}[/itex] is used sometimes for field. But mostly for finite field. So the field with 9 elements is often written as [itex]\mathbb{F}_9[/itex].

If we are working with arbitrary fields, then it seems that F, K and L are the most common notations for fields. With F standing for field, K standing for Korper (german) and L standing for Lichaam :biggrin:
 
  • #23
micromass said:
The notation [itex]\mathbb{F}[/itex] is used sometimes for field. But mostly for finite field. So the field with 9 elements is often written as [itex]\mathbb{F}_9[/itex].

If we are working with arbitrary fields, then it seems that F, K and L are the most common notations for fields. With F standing for field, K standing for Korper (german) and L standing for Lichaam :biggrin:

Ah finally someone who knows it by a name that I'm familiar with. :approve:
Won't this make you eligible for you-know-what?
Also, it gives your statement that you're living in a field a new meaning! :biggrin:
 
  • #24
I like Serena said:
Ah finally someone who knows it by a name that I'm familiar with. :approve:
Won't this make you eligible for you-know-what?
Also, it gives your statement that you're living in a field a new meaning! :biggrin:

There was once a PhD defense in my university. The title was "special places on fields", but then in dutch. The auditorium was packed until they realized that it was about mathematics.
 
  • #25
lol. Did you already post that in Lame jokes?
 
  • #26
I like Serena said:
lol. Did you already post that in Lame jokes?

It's only funny if you know dutch or german though :frown:
 
  • #27
micromass said:
It's only funny if you know dutch or german though :frown:

Well, I have to look up English words to get some of those jokes! :wink:
Having to look up a word is pretty lame, which is kind of fitting.
 
  • #28
micromass said:
There was once a PhD defense in my university. The title was "special places on fields", but then in dutch. The auditorium was packed until they realized that it was about mathematics.

:giggle:

A math PhD candidate I know just told me that as he was first preparing for the language requirement for his candidacy, he came across the word 'corps' in the paper he was reading (in french) and was confused as to what a body had to do with math.
 
  • #29
First time I saw the word "field" was when micromass used it somewhere.
I thought it was about some esoteric part of math that I never heard about.
It took some Googling before I realized that I did know it! :redface:
 

What is this symbol?

The symbol refers to a specific mathematical concept or notation used in the field of mathematics.

What is an ordered field?

An ordered field is a mathematical structure that combines the properties of both a field and an ordered set. This means that it follows the algebraic rules of a field, such as addition and multiplication, while also having a defined order for its elements.

What are the properties of an ordered field?

An ordered field must have the properties of closure, commutativity, associativity, distributivity, the existence of additive and multiplicative identities, the existence of additive and multiplicative inverses, and the property of trichotomy (any two elements can be compared).

What is the significance of an ordered field?

Ordered fields are important in mathematics because they provide a framework for analyzing and manipulating quantities that follow both algebraic and order-based rules. They are used in many areas of mathematics, including calculus, analysis, and abstract algebra.

What are some examples of ordered fields?

Some examples of ordered fields include the set of rational numbers, the set of real numbers, and the set of complex numbers. Other examples include the fields of polynomials, power series, and formal Laurent series.

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