Original post by DFranklinThe thing is, when model answers are posted, you typically reply saying "so, can I say ...", and post something that's 3 times longer, more complicated, and incorrect.
There are two things I see you doing wrong repeatedly:
Using and understanding quantifiers: There's a difference between saying something happens for a particular choice of x, versus saying it happens for every possible x. There's a difference between "saying we can choose x so that f(x, y) > 0 for every possible y", and "for every possible y, we can choose x so that f(x, y) > 0". You get these kinds of things confused.often.
Using completely unnecessary extra quantifiers / variables: You have a real habit of taking a variable or expression you know, f(x), say, and then saying "f(x) = y, where y is such that y = f(x)" (not quite that literally, but pretty close). It's unnecessary, it's confusing for the reader, and from what I can see, it is frequently confusing for yourself.
Something a maths degree should be teaching you is to be very precise in how you word your arguments. Obviously, you yourself are still learning. But the people replying to you are graduates, and although we're not perfect, we're actually pretty good at this. So when you next decide to "rephrase" one of our answers in your own words, look carefully at the differences between what you're saying and what we've written, and think about whether what you're doing actually makes any sense. Because we will have chosen the words we use, and the order in which we do things, fairly carefully.