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seen Sep 16 at 5:51

Sep
3
comment How do you simplify this radical
@MPW: Thanks... that rings a bell, but I couldn't get a solid grasp until you put it that way.
Sep
3
comment How do you simplify this radical
Why is this considered simpler? Is a radical in the numerator considered simpler than a fraction inside a radical?
Jul
2
awarded  Curious
May
27
comment What is mathematical research like?
@DisplayName, can you explain why the mathematician has hope of finding the cat? As opposed to, say, a physicist, an engineer, or an animal trainer. I'm not seeing it. The mathematician is well-versed in logic and proofs, but this won't help find the cat in the complete absence of empirical data. I think we're straying from the original point, but since I don't understand the original point it's hard to get back there. Maybe the search for the meaning of this quote is like a search for a cat that doesn't exist.
Feb
18
revised What is wrong with this equations?
attempting to improve wording
Feb
18
suggested suggested edit on What is wrong with this equations?
Feb
18
comment What is wrong with this equations?
Technically, I think you could argue that the implication could hold if $a$ happened to be equal to $b$, even when $x = 0$. How about this wording... (I'll edit the answer... rollback if you want.)
Feb
18
comment Logic puzzle: Which octopus is telling the truth?
@AviD: by definition, a hint is a statement giving information that could already be inferred from information already given. So, how can any hint not be "irrelevant" in this way? In other words, I don't see how nbubis' statement is less "relevant", or less "additional", than Ross's.
Feb
18
comment Logic puzzle: Which octopus is telling the truth?
This answer might ought to be labeled as a "what-if" scenario, as opposed to "the answer", so as not to confuse the unwary...
Feb
18
comment Logic puzzle: Which octopus is telling the truth?
@AviD: why is nbubis' statement irrelevant? Just because the same information can be inferred by a different path?
Feb
4
comment How many number of buses that the car encounter?
I guess we assume that the car goes from B to A, and the buses go from A to B?
Jan
9
comment Software for drawing geometry diagrams
That link is not very relevant... it's about drawing software in general, not about geometry diagram drawing software.
Jan
8
comment Pedagogy: How to cure students of the “law of universal linearity”?
@JordanGray: Interesting analogy. Could we then exploit that analogy to figure out appropriate pedagogy? In child development, AFAIU, the stage where children learn to apply patterns and apply them everywhere ("I eated my cereal") is considered a necessary and normal step on the way to learning where to apply each pattern. Maybe the answer to the OP's question then is like the answer to what to do if a 10-yr-old keeps saying "eated" and doesn't notice or care that it's incorrect? I don't know if that takes us anywhere helpful.
Jan
8
comment Pedagogy: How to cure students of the “law of universal linearity”?
I hope you're not saying that students should be taught not to guess, or not to develop their intuition. Rather, they need to know that their guesses need to be held humbly, and subjected to formal scrutiny when needed. I think all productive mathematicians take advantage of intuition; otherwise they'd be little better than computers. The trick is learning when formal scrutiny is needed, and when it's not.
Jan
8
comment Pedagogy: How to cure students of the “law of universal linearity”?
I was taught algebra in the US, and was taught by rules followed by examples. I would be very surprised if it were taught by examples without an explanation of the rules, though certainly one doesn't get as deep into fundamental arithmetic in 7th grade as in college. But despite being taught explicit rules, we all know that intuition is much faster and easier, so if a formal rule seems fairly intuitive, it's very tempting to pay little attention to the rule and stick with intuition. It takes pain (seeing examples where your intuition goes WRONG) to cure that habit.
Dec
21
awarded  Popular Question
Nov
23
awarded  Nice Question
Nov
6
comment Expressing as a sum of squares.
What if one of its prime factors can't be expressed as the sum of two squares?
Nov
5
comment Is math built on assumptions?
Good point about the various senses of "assume."
Nov
5
comment Is math built on assumptions?
I was going to make the same point as @ABC. And yes it does invalidate Cheyne's statement that "nothing is assumed in math." Some of the laws of logic are "on the table" in math; but the very question of whether we are able to believe our own reason is not a topic of math but of philosophy. In that sense, the validity of reasoning is assumed.