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seen Nov 21 at 5:23

Nov
12
answered Disproving existence of real root in some interval for a quintic equation
Oct
30
comment Given any computable number, is there any algorithm to decide whether it is transcendental?
@TonyK Let $X$ be the TM that takes as input $n$. It then starts enumerating all syntactically valid proofs (easy in most formal systems). For each proof, it checks if it is a proof that TM $n$ halts (easy). If so, it outputs 1. It then checks if it is a proof that TM $n$ does not halt. If so it outputs 0. Otherwise it continues running. $X$ halts on input $n$ if and only if there is a proof that says if TM $n$ halts. If for every $n$ there is a proof if TM $n$ halts, then $X$ solves Halt. As $X$ does not solve Halt, the result follows. Flaw?
Oct
29
comment Given any computable number, is there any algorithm to decide whether it is transcendental?
@TonyK Why? I can reduce my statement to yours (simply make a proof writing & checking bot for each $n$ -- if no $n$ exists for which there is no proof (it halts/does not), then my bot solves Halt. Thus there exists an $n$ for which there is no proof). I guess I do have to qualify it with a reasonable (you can mechanically verify proofs for validity, and write them) and fixed system to do the proof in.
Oct
29
comment Given any computable number, is there any algorithm to decide whether it is transcendental?
To clarify, as it took me a second: $a_n$ is transcendental iff Turing Machine $n$ halts, and $a_n$ is computable. As the halting problem cannot be solved, there exists an $n$ for which we cannot prove that Turing Machine halts, and hence an $a_n$ for which we cannot prove it is transcendental, but that $a_n$ is still computable.
Oct
17
awarded  Commentator
Oct
17
comment Limit of a 0/0 function
@NikolajK that depends on what 'is' is.
Oct
17
comment Why do we stop at exponentiation stage in arithmetic of natural numbers?
See "my number is bigger" games among mathematicians. But part of the problem is that exponentiation already grows really fast: significantly faster growing functions quickly stop talking about physically realizable numbers. Which makes applications limited.
Sep
17
revised How many ways are there to write $675$ as a difference of two squares?
added 313 characters in body
Sep
17
awarded  Teacher
Sep
17
answered How many ways are there to write $675$ as a difference of two squares?
Sep
15
comment Why exactly does the distributive property work?
@Nick the distributive property of rationals can be derived from integers, and then reals from rationals, partly due to how they are constructed. In a sense, rationals/reals are certain extensions of the natural numbers (parts of them act like natural numbers) that obey nice properties, like distributivity, because we want them to. "Because we made it so" is, however, less interesting. ;) (The naturals, naturally, are not "made" but "found", if you believe that pithy quote)
Aug
18
comment Why doesn't this converge?
@Mathmo123 Not all techniques are bothered by that: the difficulty for a particular technique to be used shouldn't be treated like a fundamental problem. It really is not the fundamental problem. The fundamental problem lies elsewhere.
Aug
18
comment Why doesn't this converge?
A function being undefined on a set of measure zero doesn't seem to be much of a barrier to integrating. As an example, integrate $1/(sgn(x) * |x^{(1/2)}|)$ from -1 to 1 -- it is undefined at 0 as well.
Aug
5
answered What are differences between affine space and vector space?
May
17
awarded  Editor
May
17
revised Extending the set of complex numbers
Mistake in associativity math, minor formatting tweaks
May
17
suggested suggested edit on Extending the set of complex numbers
Jan
15
comment Splitting a sandwich and not feeling deceived
@corsiKa if you play "honestly", you will always pick something that is "at or above average" from your own perspective. If you take into account opponent's perspectives, and they play "honestly", they will still get something "at or above average" as far as they are concerned, and so will you. If you play based on their preferences, and they play tit-for-tat to punish it, they could take something that is above average for their preferences yet force you to take something that is below average for your preferences in some cases. But that is the cost of meta gaming (you left yourself open)
Jan
15
comment Splitting a sandwich and not feeling deceived
@NoBugs each thought the risk was worth it (to wait for a chance at a bigger piece), because each could have claimed the first 1/3 of the sandwich.
Jan
15
comment Splitting a sandwich and not feeling deceived
@Mottie It handles it well. Each player divides the sandwich into equally valued pieces from their perspective. If they value meat more, pieces with meat should be smaller than pieces with less meat. If they don't care about bread at all, then they can just cut the meat up evenly, and ignore the amount of bread in each piece. The big downside is incompetence: in the two-player game, it is almost always a better idea to be the 2nd player than the 1st, because it is easier to determine which of two pieces are bigger than it is to cut something into two even pieces.