Re:Common Errors in Undergraduate Mathematics (2009)
by thaumasiotes on Sunday June 25, 2017 @05:02PM
(#14632169)
> Sure, you can (easily) provide examples where that purported identity is false, but trying to understand why was really hard for me
What do you mean by understanding why?
You can look at a graph of sqrt(x) and it's immediately obvious that sqrt(1+3) is much larger compared to sqrt(1) than sqrt(10+3) is compared to sqrt(10), but the graph is just an aggregation of an infinite number of counterexamples. The answer to "why isn't something true?" really is just a counterexample.
What "why" were you looking for beyond "that isn't a property that sqrt(x) has"?
What do you mean by understanding why?
You can look at a graph of sqrt(x) and it's immediately obvious that sqrt(1+3) is much larger compared to sqrt(1) than sqrt(10+3) is compared to sqrt(10), but the graph is just an aggregation of an infinite number of counterexamples. The answer to "why isn't something true?" really is just a counterexample.
What "why" were you looking for beyond "that isn't a property that sqrt(x) has"?