Common Errors in Undergraduate Mathematics (2009)

Re:Common Errors in Undergraduate Mathematics (2009) by dmurray on Sunday June 25, 2017 @10:32AM (#14630155)

> The answer to "Why isn't sqrt(x+y) = sqrt(x) + sqrt(y)" shouldn't be "It's not in the table of 'laws' we're allowed to use".

This is the most rigorous and correct answer I can imagine! It's not true because we have not proven it to be true or learnt it from someone who has.

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Re:Common Errors in Undergraduate Mathematics (2009) by swiley on Sunday June 25, 2017 @12:43PM (#14630855)

But it takes a lot of "playing" with math to understand the value in thinking that way. Similarly to how some people start out programming with LOGO or BASIC or bastardized javascript, people who start out in math need some extra help in order be put in the right mental place before they can think about it "correctly."

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Re:Common Errors in Undergraduate Mathematics (2009) by posterboy on Sunday June 25, 2017 @06:29PM (#14632569)

By the same line of reasoning it would be not false until we have proven it false.

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Re:Common Errors in Undergraduate Mathematics (2009) by dmurray on Monday June 26, 2017 @05:06AM (#14635211)

Yes, we should consider it neither true nor false, and not use the rule (or its negation) to prove whatever it is we actually want to prove.

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