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Sep
16
revised Find the Domain of the function: $f(x) = \frac{x^2+2x+3 }{ x^2 -9}$
added 9 characters in body
Jul
12
answered Find $ M > 0$ that for every $x > M$, we get ${{x^2 - 2x} \over {x + 2 \cos x}} >1000$
Jul
6
comment Proving logical equivalence
@Guest For the first equivalence, I used the distributive law while for the second, I used the fact that $P\land \text{ tautology}\equiv P$ (since $R\lor\neg R$ is a tautology).
Jul
6
answered Proving logical equivalence
Jul
2
awarded  Curious
Jun
22
comment basic inequality proof needed
@user3476544 [Comment now deleted by the OP] All we have proved is that if we know the $3$ inequalities about $x,x_0,y,y_0,\epsilon$ in our hypothesis are true, then it follows $|xy-x_0y_0|\le|x||y-y_0|+|y_0||x-x_0|<\epsilon$. Can you find numbers $x,x_0,y,y_0$ with $\epsilon=2$ such that $|xy-x_0y_0|=1$ and $|x||y-y_0|+|y_0||x-x_0|=3$ with all the $3$ inequalities in our hypothesis being true at the same time? You will find that it's impossible to find such numbers.
Jun
22
comment basic inequality proof needed
@user3476544 I've edited my answer. The proof is quite short, although my explanation might make it seem otherwise.
Jun
22
revised basic inequality proof needed
added 1752 characters in body
Jun
22
comment basic inequality proof needed
@user3476544 Have you applied the inequalities of $|x-x_0|$ and $|y-y_0|$ to $|x||y-y_0|+|y_0||x-x_0|$? What do you get?
Jun
22
answered basic inequality proof needed
Jun
22
answered Proposed proof of set theoretic result
Jun
16
revised HARD Arithmetic Progression Problem
added 7 characters in body
Jun
16
revised HARD Arithmetic Progression Problem
added 330 characters in body
Jun
16
answered HARD Arithmetic Progression Problem
Jun
14
answered Find the intersections of the functions
Jun
14
comment why$(\forall x \in U, P(x)) \implies (\exists x \in U, P(x))$ is false?
@yunichanyeol Yes, it is a definition. But you should convince yourself that both these definitions make intuitive sense.
Jun
14
answered why$(\forall x \in U, P(x)) \implies (\exists x \in U, P(x))$ is false?
Jun
12
answered Ice Cream Combinatorics
Jun
12
awarded  Nice Answer
Jun
12
answered How many permutations of all the letters in the word ARMADILLO begin with letter A?