Proof - counter examples, proof by exhaustion and direct proof

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This is the first video on proof for A Level Maths, covering disproof by counter example, proof by exhaustion and direct proof by deduction. I use a few examples of each, including expressions for odd/even numbers, consecutive integers and rational/irrational numbers.

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Thank you so much for this!!! Very helpful

eternityj
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Excellent. Will you be doing proof by induction, that was always a tough one for me.

tj
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Hi, love your videos! You really help me understand concepts which as a self student I sometimes find difficult!! :)
On the last example, could explain how you completed the square? When I expand (x-y)^2 I get the original expression but I'm struggling to understand why half of 2xy is just y. I'd really appreciate your help with this. Thank you for your videos they're awesome!

vikingsnowflake