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My name is Chris, and I have general interests in some things.


Nov
25
comment Are the definitions of dot product and cross product the wrong way round?
@Meelo, however, for one-dimensional vectors, $(a)\cdot(b) = ab$, which is analogous to "normal multiplication" (multiplication of real numbers). Also keep in mind that cross products are only defined for three-dimensional vectors, whereas dot products are defined for any n-dimensional vectors.
Nov
21
revised Linear transformation of normal distribution
added 2 characters in body
Oct
27
comment Use Fibonacci number to prove that is the integer that is closest to another number
You might not need to use induction for this one. You could just show that $\left|R_1\right| < \frac{1}{2}$ and that the sequence $R_n$ is geometric and convergent. That would be sufficient. (All converging geometric sequences are monotone and converge to $0$. Not counting the constant sequence $a, a, a, \dots$.)
Oct
27
comment Use Fibonacci number to prove that is the integer that is closest to another number
The base case should show that the absolute value $\left|\frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^{1}\right|<\frac{1}{2‌​}$
Oct
5
awarded  Notable Question
Oct
3
comment How to prove that the set of all countable ordinals, $\omega_1$, is uncountable / has the cardinality $\aleph_1$?
@AsafKaragila You're right, I just read that cardinals are defined as ordinals after posting my comment... ::foot in mouth:: Still, making the edit would help clear the confusion. However I disagree that it is "overreaching." In my opinion, a question that can be improved should, no matter how old, especially for users who so happen to stumble upon it years later.
Sep
30
revised How to prove that the set of all countable ordinals, $\omega_1$, is uncountable / has the cardinality $\aleph_1$?
changed "least uncountable cardinal" to "least uncountable ordinal" but had to add "number" to meet the 6-character requirement
Sep
30
suggested suggested edit on How to prove that the set of all countable ordinals, $\omega_1$, is uncountable / has the cardinality $\aleph_1$?
Sep
30
comment How to prove that the set of all countable ordinals, $\omega_1$, is uncountable / has the cardinality $\aleph_1$?
@Levon I believe your second sentence should read, "$\omega_1$ is usually defined to be the least uncountable ordinal." Making this edit would clear up some confusion in the comments. As a matter of fact, $\omega_1$ technically isn't a cardinal number. When referring to the least uncountable cardinal, mathematicians typically use $\aleph_1$.
Sep
30
awarded  Explainer
Sep
29
accepted Prove this function is pointwise continuous
Sep
29
revised Are all the points in a nonempty open set limit points?
added Case 2: delta is less than epsilon
Sep
29
revised Are all the points in a nonempty open set limit points?
edited body
Sep
29
suggested suggested edit on Are all the points in a nonempty open set limit points?
Sep
29
answered Are all the points in a nonempty open set limit points?
Sep
24
awarded  Autobiographer
Sep
21
comment Proving of Inequalities
Please add the different methods you've tried. It helps to see what work you've done first, and it makes your question more useful.
Sep
19
revised Prove this function is pointwise continuous
deleted 56 characters in body
Sep
19
answered Prove this function is pointwise continuous
Sep
19
revised Prove this function is pointwise continuous
deleted 295 characters in body