Hey there Sign in to join this conversationNew here? Join for free

Co-prime Notation

Announcements Posted on
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    Quick question. Say you're proving \sqrt 3 is irrational or something similar, can you express \mathrm{gcd(a,b)=1} as a  \perp  b? We weren't taught the notation, so not sure if I'm using it correctly.
    • 3 followers
    Offline

    I've never seen it before, but Wikipedia appears to use it. Personally I write (a,b) instead of \text{gcd}(a,b), and so I'd just write (a,b)=1. Little confusion will be caused by this notation in a number theoretic context.
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    (Original post by nuodai)
    I've never seen it before, but Wikipedia appears to use it. Personally I write (a,b) instead of \text{gcd}(a,b), and so I'd just write (a,b)=1. Little confusion will be caused by this notation in a number theoretic context.
    Ah, I thought it might be standard notation and wanted the proof to look a bit more professional. Perhaps I should stick to the former if he hasn't taught it this way.
    • 3 followers
    Offline

    (Original post by Brit_Miller)
    Ah, I thought it might be standard notation and wanted the proof to look a bit more professional. Perhaps I should stick to the former if he hasn't taught it this way.
    If you're doing something for uni (e.g. exam, coursework), don't introduce notation which isn't in your course unless you explain what it is first. If you were to say "write a \perp b to denote \text{gcd}(a,b)=1" then that would be fine, but you shouldn't assume that an examiner will know what you mean if the notation isn't introduced in your lecture notes.
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    (Original post by nuodai)
    If you're doing something for uni (e.g. exam, coursework), don't introduce notation which isn't in your course unless you explain what it is first. If you were to say "write a \perp b to denote \text{gcd}(a,b)=1" then that would be fine, but you shouldn't assume that an examiner will know what you mean if the notation isn't introduced in your lecture notes.
    Aye, I'll definitely just use the former. Thanks for the help!
    • 2 followers
    Offline

    ReputationRep:
    (Original post by Brit_Miller)
    Ah, I thought it might be standard notation and wanted the proof to look a bit more professional. Perhaps I should stick to the former if he hasn't taught it this way.
    Professional mathematical writing eschews excessive symbology. It is a common mistake of the amateur to try and abbreviate everything. Nothing looks worse than, for example, statements abbreviated like the following: \forall a,b \in \mathbb{Z}, \exists ! c \in \mathbb{Z} \mbox{ such that... } etc.

    Just write 'a and b are coprime.'
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    (Original post by Jake22)
    Professional mathematical writing eschews excessive symbology. It is a common mistake of the amateur to try and abbreviate everything. Nothing looks worse than, for example, statements abbreviated like the following: \forall a,b \in \mathbb{Z}, \exists ! c \in \mathbb{Z} \mbox{ such that... } etc.

    Just write 'a and b are coprime.'
    Why do they teach us to write like that then? :confused:
    • 2 followers
    Offline

    ReputationRep:
    (Original post by Brit_Miller)
    Why do they teach us to write like that then? :confused:
    For the purpose of making short hand notes or writing on blackboards. Quantifiers also have their use in defining, say, a predicated set that involves more than one quantifier.

    I mean, you were presumably taught at primary school that one can abbreviate 'and' by using the ampersand symbol. I am sure that you were also made aware that in an essay or suchlike, you were still expected to use the full word 'and' rather than '&'. Same rules apply.

    I don't think that anyone would suggest that you hand in a piece of written work with, for example, sentences that start with symbols.

    Look in any maths book. They mostly use words - not just a collection of symbols. In the statement of lemmata, propositions and theorems in particular, one tends to use symbols and abbreviations only where it saves a lot of space and makes for increased readability.
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    (Original post by Jake22)
    For the purpose of making short hand notes or writing on blackboards. Quantifiers also have their use in defining, say, a predicated set that involves more than one quantifier.

    I mean, you were presumably taught at primary school that one can abbreviate 'and' by using the ampersand symbol. I am sure that you were also made aware that in an essay or suchlike, you were still expected to use the full word 'and' rather than '&'. Same rules apply.

    I don't think that anyone would suggest that you hand in a piece of written work with, for example, sentences that start with symbols.

    Look in any maths book. They mostly use words - not just a collection of symbols. In the statement of lemmata, propositions and theorems in particular, one tends to use symbols and abbreviations only where it saves a lot of space and makes for increased readability.
    Our lecturer actually encouraged us to write our proofs using all the shorthand notation - though they're only short proofs. Maybe it's just to make sure we understand what they mean and use them correctly.
    • 2 followers
    Offline

    ReputationRep:
    (Original post by Brit_Miller)
    Our lecturer actually encouraged us to write our proofs using all the shorthand notation - though they're only short proofs. Maybe it's just to make sure we understand what they mean and use them correctly.
    I would guess that your last sentence is the motivation - he is treating it as an exercise in familiarising yourselves with the notation.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?

    this is what you'll be called on TSR

  2. this can't be left blank
    this email is already registered. Forgotten your password?

    never shared and never spammed

  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide the button to the right to create your account

    Slide to join now Processing…

Updated: May 9, 2012
New on TSR

Talk about SQA results day

Join the chat ahead of grades coming out on Tuesday

Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.