Reputation
963
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
1 9 29
Newest
 Yearling
Impact
~67k people reached

Sep
25
comment Why are the derivatives of these two equations different?
@SamWeatherhog you absolutely do lose information. Here's another example: given $a=b$, you might decide to square both sides and share the modification. Someone else, receiving $a^2=b^2$ and not having the original equation, might offer $a=2$, $b=-2$ as a solution. This clearly satisfies the modified but does not satisfy the original. Some information from the original equation is lost when squaring both sides.
Sep
24
comment Why are the derivatives of these two equations different?
You lose information by manipulating the equation. In the original, you are guaranteed $x\not=y$. In the manipulated version, this fact is not absolutely certain.
Sep
12
comment Is it possible to plot a graph of any shape?
check out desmos.com
Sep
12
comment If a function is undefined at a point, is it also discontinuous at that point?
@KristofferRyhl or what the person could have meant was that the limit exists at $1$. a lot of students (incorrectly) think that if the limit of a function exists at $c$ then it's continuous at $c$.
Sep
8
revised When is equality not reflexive?
formatting changes
Sep
8
revised When is equality not reflexive?
added 67 characters in body
Sep
8
comment When is equality not reflexive?
Since your question only mentions symmetry and not reflexivity, I assume the title of your question, "When is equality not reflexive?" is a typo. Please clarify.
Sep
8
answered When is equality not reflexive?
Sep
3
awarded  Yearling
Aug
30
awarded  Famous Question
Aug
21
comment Prove or disprove: a closed, non-open set is also bounded
@Bernard that may be true, but I think it depends on the author. My book uses the limit point definition. Incidentally I think it's much more fascinating to define two concepts separately and then prove that they're related. E.g. define $\ln(x)$ as an integral and $\exp(x)$ as a summation, then prove that they're inverse functions (rather than defining one as the inverse of the other).
Aug
20
comment Prove or disprove: a closed, non-open set is also bounded
a set is closed iff it contains all its limit points
Aug
20
comment Prove or disprove: a closed, non-open set is also bounded
Good answer; the only thing that would make me happier is if you used the definition of closed to prove it is closed. (Not that proving its complement is open isn't a valid proof, but I like a more direct approach.)
Aug
20
comment Prove or disprove: a closed, non-open set is also bounded
@NigelOvermars WolframAlpha says the right end is open. But it does contain all its limit points…
Aug
20
asked Prove or disprove: a closed, non-open set is also bounded
Aug
8
revised Why $\int \frac{dx}{\sqrt{9-x^2}} = sin^{-1}\frac{x}{3}$?
removed blockquotes
Aug
8
suggested approved edit on Why $\int \frac{dx}{\sqrt{9-x^2}} = sin^{-1}\frac{x}{3}$?
Aug
3
comment Are the Real numbers really Complete?
@MarkS. — very interesting. any links to further reading on this?
Aug
2
revised How many ways are there to define sine and cosine?
formatting and spelling
Aug
2
comment The relation x=1
… and thus $x=y$. That last part is key for antisymmetry.