Results 1 to 15 of 15

Math Help - provided that

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    158

    provided that

    What does "provided that" mean in terms of logic symbols? Is it a conditional implication (=>) or a biconditional implication(<=>)? I see it used primarily as a biconditional implication but sometimes (in the same book) it appears as though it is being used as a conditional implication.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    If I say "A provided that B", I generally mean that if A is true, it must be that B is true. Doesn't that make sense? So that would translate to A => B. Context is always important, however.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    158
    I sometimes come across: A ==> B, provided that C
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,962
    Thanks
    1784
    Awards
    1
    Quote Originally Posted by Noxide View Post
    What does "provided that" mean in terms of logic symbols? Is it a conditional implication (=>) or a biconditional implication(<=>)? I see it used primarily as a biconditional implication but sometimes (in the same book) it appears as though it is being used as a conditional implication.
    A provided B, means that A happens only if B happens.
    “A only if B “ means “If A then B”.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Feb 2010
    Posts
    466
    Thanks
    4
    delete
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,561
    Thanks
    785
    Am I the only one who thinks that "A provided that B" means B => A? In my opinion, this is equivalent to "A assuming that B" and one usually assumes hypotheses, not conclusions...

    This Wikibooks page has the same opinion. (Consider it as a sanity check, not necessarily as an authoritative source.)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Feb 2010
    Posts
    466
    Thanks
    4
    It might be a peculiar subtlety of English.

    "A provided that B" suggests to me "A -> B"

    but

    "If we are provided B then we have A" suggests to me "B -> A".

    Example:

    "I'll give you an apple provided that you give me a banana" would likely be taken as "I won't give you an apple unless you give me a banana", i.e. "A -> B"

    but

    "If we are provided that 'I give you give me a banana' is true then 'I give you ana apple' is true" means "If you give me a banana then I give you an apple", i.e., "B -> A".
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by emakarov View Post
    Am I the only one who thinks that "A provided that B" means B => A? In my opinion, this is equivalent to "A assuming that B" and one usually assumes hypotheses, not conclusions...

    This Wikibooks page has the same opinion. (Consider it as a sanity check, not necessarily as an authoritative source.)
    I thought the same thing, but then started to doubt my thoughts...
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,962
    Thanks
    1784
    Awards
    1
    Surely “A provided B” means “B is necessary for A”.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Sep 2009
    Posts
    158
    The site says that "provided" can be swapped for if and is equivalent to p => q
    and that "only provided" can be swapped for (if and only if)

    I guess my problem now lies in the ambiguity that this causes.

    for example

    two nonzero vectors v and w are perpendicular if the dot product of v and w is equal to zero
    In this case if means if and only if
    and often do i see provided being used in this way, i.e.
    two nonzero vectors v and w are perpendicular provided that the dot product of v and w is equal to zero

    so, you can see my problem (or my rage at people who choose to use this word) is there a definitive way to use provided?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by Noxide View Post
    The site says that "provided" can be swapped for if and is equivalent to p => q
    and that "only provided" can be swapped for (if and only if)

    I guess my problem now lies in the ambiguity that this causes.

    for example

    two nonzero vectors v and w are perpendicular if the dot product of v and w is equal to zero
    In this case if means if and only if
    and often do i see provided being used in this way, i.e.
    two nonzero vectors v and w are perpendicular provided that the dot product of v and w is equal to zero

    so, you can see my problem (or my rage at people who choose to use this word) is there a definitive way to use provided?
    If and only if is not used here because this is a definition, not a theorem. You're saying `if this happens then I'll call it this'.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,561
    Thanks
    785
    is there a definitive way to use provided?
    Yes: not to use it (PDF document).
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Member
    Joined
    Sep 2009
    Posts
    158
    Quote Originally Posted by Swlabr View Post
    If and only if is not used here because this is a definition, not a theorem. You're saying `if this happens then I'll call it this'.

    That's just completely wrong. Those two statements are equivalent and by convention if is used to denote if and only if when used in a definition.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Quote Originally Posted by Noxide View Post
    That's just completely wrong. Those two statements are equivalent and by convention if is used to denote if and only if when used in a definition.
    And conventions differ between different people. I, for one, have never seen definitions use "if and only if".
    Follow Math Help Forum on Facebook and Google+

  15. #15
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    For me, definitions are always if-and-only-if. Sometimes it's explicit; but if not, I've always understood that feature to be implicit.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The number provided for each value
    Posted in the Math Software Forum
    Replies: 1
    Last Post: May 8th 2010, 03:16 AM
  2. Replies: 2
    Last Post: February 11th 2010, 03:39 AM
  3. Is the answer provided wrong!?
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 29th 2010, 07:35 AM
  4. Replies: 0
    Last Post: November 3rd 2008, 05:49 PM
  5. Replies: 3
    Last Post: May 8th 2008, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum