Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

n

------

x - y

= or not =

n+y

------

x

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,464

By ----- do you mean divide?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,269

hi

You only need one counter example to prove it is false. Try choosing some numbers for n, x and y.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,464

If you do, it's false. Counterexample: n, x is 2, y is 1

2/(2-1) doesn't equal (2+1)/2

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

ShivamS wrote:

If you do, it's false. Counterexample: n, x is 2, y is 1

2/(2-1) doesn't equal (2+1)/2

This is proof by what? So you only need one instance of a counterexample to prove it's false but you need to use variables to prove something is true. Well I found I found some numbers that made it true and I was going to use it to solve a problem but realized that it might not be true for all numbers and turns out it isn't.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,464

To prove it false, you need only one counterexample. To prove it true, there are several methods like contradiction, induction. A great book on proofs is How to Prove It: A Structured Approach by Daniel J. Velleman.

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