Math Prove or Proof

Discussion in 'Other Pre-University Math' started by nycmathguy, Jul 17, 2021.

  1. nycmathguy


    Jun 27, 2021
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    What's the difference between math prove and math proof?

    Sample A

    Prove the trig identity. Why not proof the trig identity?

    Sample B

    Proof inequality by induction. Why not prove inequality by induction?

    I am not talking about working out math problems here. I need to know when to use prove and when to use proof.
    nycmathguy, Jul 17, 2021
  2. nycmathguy


    Jun 27, 2021
    Likes Received:
    prove: means demonstrate the truth or existence of (something) by evidence or argument

    example: "you will be asked to prove your identity" (means you will need your photo ID)

    proof: evidence or argument establishing or helping to establish a fact or the truth of a statement.
    "you will be asked to give proof of your identity" (means you will need to give photo ID)

    example in math
    Theorem 3.1.
    Prove √3 is irrational

    Suppose not; i.e., suppose √3 element Q.
    Then some value of m, n element Z with m and n relatively prime and √3 =m/n.
    Then 3 = m^2/n^2, or 3n^2 = m^2.

    Thus m^2 is divisible by 3 so by Theorem 2.1, m is also. By definition, m = 3k for some k element Z. Hence m^2 = 9k^2 = 3n^2 and so 3k^2 = n^2.
    Thus n^2 is divisible by 3 and again by Theorem 2.1, n is also divisible by 3.
    But m, n are relatively prime, a contradiction.
    Thus √3 not element Q.
    MathLover1, Jul 17, 2021
    nycmathguy likes this.
  3. nycmathguy


    Jun 27, 2021
    Likes Received:
    Prove lies in the question. The actual work to show what must be proven is the proof.
    nycmathguy, Jul 18, 2021
    MathLover1 likes this.
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