Oxbridge Maths (and related subjects) APN, January 2012
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A proof that 1 = 2 Step 1: Let a = b. Step 2: Then a 2 = ab. Step 3: So a 2 + a 2 = a 2 + ab. Step 4: In other words 2a 2 = a 2 + ab. Step 5: So2a 2 – 2ab = a 2 + ab – 2ab Step 6: and 2a 2 – 2ab = a 2 – ab. Step 7: So 2(a 2 – ab ) = a 2 – ab. Step 8: Cancelling the (a 2 – ab) from both sides gives 1 = 2.
Correct procedure in equations
Example for discussion Solve for x the following equations, commenting upon any special cases that arise in the two cases. (i) ax + b = bx + c (ii) ax + a 2 = b 2 – bx
STEP and AEA Principles how to write mathematics in “good style” understanding key symbols and using them correctly ‘exact’ values reasoning, conciseness and clarity
Common symbols to use:
Week 1: Problems to bite on Please see handout.