925 reputation
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location Grand Rapids, MI
age 21
visits member for 3 years, 3 months
seen 15 hours ago

I am a recent graduate of Grand Valley State University.


Sep
25
comment Is it true to say that “it's not logically possible to prove something can't be done”?
It looks like you're interpreting Asok's "can't be done" as "can't be proved within a formal system". I don't see any evidence that Asok is talking about formal systems; what's your reasoning?
Sep
2
answered Having hard time understanding proofs by contradiction.
Aug
31
comment How many subsets does the set $\{1, 2, \dots , n\}$ have that contain no two consecutive integers if $1$ and $n$ also count as consecutive?
Well, it's the number of subsets that don't contain two consecutive integers, minus the number of subsets that don't contain two consecutive integers but do contain both $1$ and $n$.
Aug
13
awarded  Nice Answer
Aug
12
comment Proof of Existence of Algebraic Closure: Too simple to be true?
Answer to first question: "A is strictly smaller than B" means that there is no surjective function from A to B. Answer to second question: yes, it is; this shows that the collection of algebraic extensions of $K$ is not a small class.
Aug
12
answered Proof of Existence of Algebraic Closure: Too simple to be true?
Aug
12
answered A question regarding irrational lengths in reality
Jul
19
awarded  Yearling
Jul
2
awarded  Curious
Jun
9
comment 'Obvious' theorems that are actually false
This is Leibniz's Law of Continuity, right?
Jun
9
comment 'Obvious' theorems that are actually false
I wonder how "obvious" this is among people who know how the real numbers are actually defined.
Jun
9
comment 'Obvious' theorems that are actually false
By "chain", do we mean a collection of subsets of N that is totally ordered by the subset relation? You can represent the interval $[0, 1]$ as such a chain. For each number $x$ in that interval, the subset contains (rounding down) the first $9x$ one-digit numbers, the first $90x$ two-digit numbers, the first $900x$ three-digit numbers, and so on.
Jun
3
comment Turning a closed-form generating function back to ordinary power series
For rational functions, the easiest way to find a power series is probably to use long division. Rewrite $a/b$ as $(a-cb)/b + c$, where $c$ is the quotient of the lowest-degree terms of $a$ and $b$. Repeat ad nauseam.
Apr
15
comment What about generlizing grammars?
I think this question ("given some examples, how can you determine what the rule may be?") is essentially what the entire field of machine learning tries to answer. I don't know how to give a better answer than "I suggest reading a machine learning textbook".
Apr
15
comment How do I compute Euler phi function efficiently for repeated prime factors?
Note that computing the phi function may be prohibitively difficult if you don't know the number's prime factorization. If $p$ and $q$ are prime numbers, and we know what $pq$ and $\phi(pq)$ are, we can find what $p$ and $q$ are.
Apr
15
answered How do I compute Euler phi function efficiently for repeated prime factors?
Apr
13
comment Visually deceptive “proofs” which are mathematically wrong
@16807 Now, suppose that there are a million doors, with a car behind one and a door behind all the others. Monty Hall goes into a flying rage and randomly kicks down 999,998 doors, and they all happen to have goats behind them. What's the probability that the door you originally picked has a car behind it? The answer is 50%.
Apr
9
awarded  Promoter
Dec
16
comment Monty hall problem extended.
Note that this is only true if Monty intentionally chooses doors with goats. If you pick an arbitrary door, and Monty randomly opens 999,998 doors, and all of them happen to be goats, the probability of the car being behind each door is now 1/2.
Oct
18
comment Riddle: 1 question to know if the number is 1, 2 or 3
I don't agree that we know that 1/0 is not a frog. If I define 1/0 as being a certain individual frog, then my definition doesn't contradict any mathematical theorem. It's not an invalid definition; it's merely a silly and nonsensical one. And doesn't "undefined" just mean "not having a valid, agreed-upon definition"?