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What does the 'not equal to' sign mean?

  1. Feb 21, 2008 #1
    the 'not equal to' sign ( =/= )? If I say, blue =/= red. could you simply say: blue = 0 red? Or: life =/= death... mean life = 0 death? Does the not equal to sign mean merely 'incompatible' or does it mean 0 of the thing =/=?

    How do you use that sign?! I may be far off
     
    Last edited: Feb 21, 2008
  2. jcsd
  3. Feb 21, 2008 #2
    It simply means that the two objects are not equivalent. It is not valid to derive any equalities from that statement. For example, 2 [itex]\ne[/itex] 3 does not imply that 2 = 0*3 = 0.
     
  4. Feb 21, 2008 #3
    then what is the 'not equal to' sign used for. Progamming?

    And not equal to what? What if i had a statement blue =/= red... pretty much means blue and red are logically incompatible. Almost like there is 0 red in blue and 0 blue in red. But thats not the function of Not equal to? Not equal to is only 'not equivalent'?

    don't forget my question above.
     
  5. Feb 21, 2008 #4

    chroot

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    Sometimes it's just as useful to know two things are not equal as it is to know two things are equal.

    - Warren
     
  6. Feb 21, 2008 #5

    CRGreathouse

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    It means "not equal", not "incomparable". 2 is comparable to 3 (in particular, 2 < 3), but they aren't equal. Incomparable things should be not equal -- as in apple =/= 7 -- but then again maybe not... aleph_1 is incomparable to beth_1 in ZFC, but the statement that aleph_1 =/= beth_1 can't be proven in ZFC (since aleph_1 is equal to beth_1 in some models of ZFC, namely those with the continuum hypothesis).
     
  7. Feb 21, 2008 #6
    The expression "blue =/= red" is basically shorthand for "it is not the case that blue=red." You can draw no other conclusions from it.
     
  8. Feb 22, 2008 #7
    The "not equal sign" isn't really used in the context you are trying to use it for.. saying blue does not equal read is not same as blue equals zero red. It's actually means literally "not equal" as in two things are not equal to eachother. You are attempting to over analyze the meaning.
     
  9. Feb 22, 2008 #8
    This may be too philosophical for this forum. contextually there is 0 so it has actual math. But I believe the idea is out of mathematical context, more philosophical.

    1) 'not equal to' = no (ex. not equal to blue = no blue)
    2) no blue = 0 blue
    3) therefore, 0 = 'not equal to'
     
  10. Feb 22, 2008 #9

    By your logic...

    Would you say that purple =/= blue?

    If so, then purple = 0 blue?

    This simply is not true, purple is made of blue and red, so it must have some blue in it right?

    Not equal to in no way implies zero of something or zero in anyway. It just means that two objects are not the same exact thing. I think Manchot hit the nail on the head with his definition, you can not draw any other conclusions.
     
  11. Feb 22, 2008 #10
    diffy, this may be hard for you. but it either equals blue or it does NOT equal blue. There's no inbetween.
     
  12. Feb 22, 2008 #11
    Ad hominem. I see no problem with Diffy's reply.
     
  13. Feb 22, 2008 #12
    Thanks for insulting me, that's fantastic.

    There is no relationship between the 'does not equals sign', and the number 0.

    You can't say that, I'll go for reductio ad absurdum this time. Because then Green =/= red would imply that Green = 0 Red by the same logic. So now we have Blue = 0 Red, and Green = 0 Red, so by transitive Blue = Green.
     
  14. Feb 23, 2008 #13
    To be honest, I have no idea what kinkaid is trying to do with the number 0 and [tex]\neq[/tex], but it reminds me a bit of how some programming languages such as C/C++ and Perl treat true and false.

    In C/C++ and Perl, a true comparison is assigned the number 1 and a false comparison is assigned the number 0 (and any other integer is also consider false). However, it doesn't change anything inside of the comparison at all, it assigns the number to the entire comparison.

    I.e, (A != B) is either 0 or 1 (depending on whether it's false or true respectively). This also has no mathematical basis; true and false cannot be considered integers. It is just how the results of operations are stored in memory, and giving the programmer access to this lets him do a few tricks to optimize the program.

    But I've never before seen anyone get confused by this and think that this treatment of true and false had any mathematical relevance.

    ----

    kinkaid, you said "it has 0 so it has actual math". However, you don't need numbers to do math. There are in fact a lot of branches of mathematics that don't have any numbers in the basic theory at all and don't depend on the existence of numbers as we usually think of them in any way. For instance, look up Group theory. While some familiar sets of numbers form groups, so do a lot of things that have no numbers in them at all.
     
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