Math question:proving.

• Jia Xun

  17 Jan 12, 20:27

  Don't laugh please,I'm interested to know the answer.

  Prove that 1+1=2 or vice versa.

  Any plausible answer would be appreciated.:)

  Thanks.^_^

• Summer hill

  17 Jan 12, 21:21

  I give you 1 apple.

  And later ur Dad give another apple(considering u had not eat the apple i gave u)

  how many apples u have now?

• Darkness_hacker99

  18 Jan 12, 01:22

  it makes me remind of a very maths question... I can't remember the exact question, but it's also similar to proving an algebra.  I think it's in the forum, but I just can't find it...

• frekiwang

  18 Jan 12, 06:28

  It cannot be proven as it is not an identity but a definition.

  We define 2 to be equal to two '1's and 3 to be equal to three '1's and so on.

  So things like 1+1=2, 1+1+1=3 cannot be proven. 

  However, using these definitions, we can prove 2 + 1 = 3.

   

  If we define 3 to be equal to two '1's, we will have 1 + 1 = 3, so the result solely depends on how we define our numbers.

   

  You will learn something similar at University level if Maths/Applied Maths is your major.

• wee_ws

  18 Jan 12, 07:58

  Hi,

    Indeed, as frekiwang has highlighted, proofs of results are (always) built from definitions and axioms which are statements that are true or assumed to be true.

    Just like theorems in geometry were established by using Euclid's five axioms.

    Thanks.

  Cheers,
  Wen Shih

• Jia Xun

  18 Jan 12, 19:56

  Alright,thanks a lot.:)Will read up on that when I have the time.

  Maybe next time we can change the assumption to a real proof.^_^

• wee_ws

  18 Jan 12, 20:42

  Hi Jia Xun,

    Mathematicians have tried to prove Euclid's fifth postulate:

    http://www.cut-the-knot.org/triangle/pythpar/Attempts.shtml

    One must start with something that is true, then build up the rest from there. This is the way to move ahead :)

  Cheers,
  Wen Shih

• wee_ws

  18 Jan 12, 20:53

  Hi,

    Here are some proof methods taught in schools:

    1. Direct proof (e.g., trigonometric identities);

    2. Proof by contradiction (e.g., tangent does not meet the curve again);

    3. Proof by mathematical induction (e.g., results involving summations).

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  18 Jan 12, 20:59

  Hi,

    Just for laughs:

    http://www.themathlab.com/geometry/funnyproofs.htm

    I have seen method 29 used by students:

    Since the first three terms are in an arithmetic progression, therefore the sequence is an arithmetic progression.

    Thanks.

  Cheers,
  Wen Shih