[Challenge] Prove (-1) * (-1) = 1

• CoolMyth

  13 Feb 06, 00:33

  Ever thought why this is true? Now try your hand at proving it.
  
  Some hints:
  
  Let a, b and c be numbers and -a, -b and -c be its negative respectively.
  
  i) a + (-a) = 0 (Obvious, right? )
  
  ii) a*(b+c) = a*b + a*c
  
  iii) a + c = b + c <--> a = b
  
  Okay, now try proving (-1) * (-1) = 1 using the above hints. But in your proof, don't ever use (-1) * (-1) = 1.
• hisoka

  13 Feb 06, 00:43

  Originally posted by CoolMyth:

  Ever thought why this is true? Now try your hand at proving it.
  
  Some hints:
  
  Let a, b and c be numbers and -a, -b and -c be its negative respectively.
  
  i) a + (-a) = 0 (Obvious, right? )
  
  ii) a*(b+c) = a*b + a*c
  
  iii) a + c = b + c <--> a = b
  
  Okay, now try proving (-1) * (-1) = 1 using the above hints. But in your proof, don't ever use (-1) * (-1) = 1.

  erm ok use 1 and 2
  
  b=a and c = -a
  
  so a^2 +a(-a) = 0
  
  a^2= (-1).(-1).a^2
  
  therefore (-1).(-1) = 1??
• CoolMyth

  13 Feb 06, 00:54

  Originally posted by hisoka:

  erm ok use 1 and 2
  
  b=a and c = -a
  
  so a^2 +a(-a) = 0
  
  a^2= (-1).(-1).a^2
  
  therefore (-1).(-1) = 1??

  By shifting the part in red to the other side, you're indirectly implying that
  
  1 = -(-1) = (-1) * (-1), which is the question itself.
  
  So, it's not correct, sorry, but it's a good effort.
  
  Note, a, b and c are just numbers, you're supposed to substitute appropriate values for them and use the hints given.
  
  
• hisoka

  13 Feb 06, 01:13

  Originally posted by CoolMyth:

  By shifting the part in red to the other side, you're indirectly implying that
  
  1 = -(-1) = (-1) * (-1), which is the question itself.
  
  So, it's not correct, sorry, but it's a good effort.
  
  Note, a, b and c are just numbers, you're supposed to substitute appropriate values for them and use the hints given.
  
  

  huh?? dun get what you mean
  
  what i did was to add both sides with the term i wanna appear on the right so no implied of the 1 =-(-1)
• CoolMyth

  13 Feb 06, 01:32

  Originally posted by hisoka:

  huh?? dun get what you mean
  
  what i did was to add both sides with the term i wanna appear on the right so no implied of the 1 =-(-1)

  EDIT: Finally saw something wrong.
  
  Okay. Here's how it goes:
  
  You were actually using the fact that (-1)a = -a, which is not of my hints given.
  
  Sorry.
  
  
• hisoka

  13 Feb 06, 01:35

  Originally posted by CoolMyth:

  EDIT by mod: see above

  wrong marking request to strip you of job
• CoolMyth

  13 Feb 06, 01:46

  Proof of (-1)*a = -a. (Different from question)
  
  From a + (-a) = 0
  
  --> [a + (-1)*a] + (-a) = (-1)*a (Add (-1)*a on both sides)
  
  --> [a(1 + (-1)] + (-a) = (-1)*a
  
  --> a*0 + (-a) = (-1)*a
  
  --> 0 + (-a) = (-1)*a
  
  --> (-1)*a = -a
• ndmmxiaomayi

  14 Feb 06, 20:57

  I'm stumped.
• hisoka

  14 Feb 06, 21:13

  Originally posted by CoolMyth:

  EDIT: Finally saw something wrong.
  
  Okay. Here's how it goes:
  
  You were actually using the fact that (-1)a = -a, which is not of my hints given.
  
  Sorry.
  
  

  you never say cannot use other such terms wor
• CoolMyth

  14 Feb 06, 22:32

  Originally posted by hisoka:

  you never say cannot use other such terms wor

  I got say use the above hints mah.
  
  Then you used another one....
  
  Okay lah, correct lah, correct lah. Happy?