562 reputation
521
bio website google.com/+chrisharvey2pi
location
age
visits member for 2 years, 11 months
seen Aug 15 at 4:02

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


Aug
15
comment What is the cardinality of the countable ordinals?
Question: Take the set of all finite ordinal numbers $\{1,2,3,\dots\}$. Its cardinality is $\aleph_0$ right? Now, the set of all countable ordinal numbers includes exactly all finite ordinal numbers plus the element $\aleph_0$, right? IOW, the set of all countable ordinals is $\{1,2,3,\dots\}\cup\{\aleph_0\}$. It seems to me that the cardinality of this set is the sum of the cardinality of each part, which is $\aleph_0 + 1$, which is still $\aleph_0$. So why is it $\aleph_1$?
Jul
9
awarded  Notable Question
Jul
3
comment Alternative definition of complex number, showing it is equivalent to the tradidional one.
The problem with starting out with the definition $i^2=-1$ is that you must assume there exists some value $i$ first. We are not yet guaranteed such an existence.
Jul
3
comment How to draw the graph of this function? (very difficult)
preview: desmos.com/calculator/j8l7qzfvka
Jul
2
awarded  Curious
Jun
18
comment Prove there exists a unique $n$-th degree polynomial that passes through $n+1$ points in the plane
Any arbitrary 3 points, then.
Jun
18
comment Prove there exists a unique $n$-th degree polynomial that passes through $n+1$ points in the plane
@AndréNicolas Not true. Given the points $(0,0)$, $(1,1)$, and $(2,3)$, there does not exist a 1st degree polynomial (a line) that goes through all 3 points. Did you mean "$\ge$"?
Jun
17
revised Prove there exists a unique $n$-th degree polynomial that passes through $n+1$ points in the plane
added further readings
Jun
17
asked Prove there exists a unique $n$-th degree polynomial that passes through $n+1$ points in the plane
May
5
awarded  Notable Question
May
2
revised What are arguments to $\frac 00 = Undefined$?
added case
May
2
comment What are arguments to $\frac 00 = Undefined$?
@KeshavSrinivasan wow, you lost me on that last part. What did you mean by "measures are only countably additive?"
Apr
10
awarded  Popular Question
Feb
4
revised What are arguments to $\frac 00 = Undefined$?
changed cases 1 and 2
Feb
4
comment What are arguments to $\frac 00 = Undefined$?
@Gaffney only if you're working in certain types of algebra systems. In high school algebra though, $0/0$ is undefined, not an arbitrary real number.
Feb
4
answered What are arguments to $\frac 00 = Undefined$?
Feb
4
comment What are arguments to $\frac 00 = Undefined$?
In your second scenario (John has 0 apples and divides them to 5 friends), the mathematical expression that would model the situation would be $0/5$, which is indeed $0$. However, if you are trying to model $5/0$, try a problem like this: "John has 5 apples, and divides them evenly to 0 friends. How many apples does each friend get?" The answer is surely not 0. It's undefined.
Feb
1
comment How to prove that the set of rational numbers are countable?
Duplicate of math.stackexchange.com/questions/95731/…
Feb
1
comment How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
Duplicate of math.stackexchange.com/questions/95731/…
Jan
29
revised Get rid of an existential quantifier
improved readability, fixed delimiter size