• October 9th, 2019, 18:16
Yes, something like that. Of course, if you write an actual Turing machine, it would require a bit more care and perhaps debugging.
4 replies | 91 view(s)
• October 9th, 2019, 17:17
Of course. There are programs called interactive theorem provers, or proof assistants, where you can construct proofs in Peano Arithmetic.
6 replies | 363 view(s)
• October 9th, 2019, 15:32
Are you using a machine with two heads? A standard TM has only one head. You could mark symbols one by one from the beginning and the end of the...
4 replies | 91 view(s)
• October 9th, 2019, 15:23
Your question makes little sense to someone unfamiliar with how Turing machines are coded as numbers in your course. You probably realize that there...
3 replies | 74 view(s)
• October 8th, 2019, 17:27
In the book Peter Smith. An Introduction to Gödel's Theorems. Cambridge University Press: 2013 the description of BA on p. 62 includes...
6 replies | 363 view(s)
• October 8th, 2019, 01:50
Thanks for the help, HallsofIvy .... However I still think my calculation of z_2 ... that is z_2 = 2^{ \frac{1}{4} } e^{ - i \frac{ \pi }{8} } is...
3 replies | 309 view(s)
• October 7th, 2019, 17:29
For each $b\in B$ choose a single $a_b\in A$ such that $f(a_b)=b$. Then consider the restriction of $f$ to $A'=\{a_b\mid b\in B\}$. Show that this is...
1 replies | 113 view(s)
• October 7th, 2019, 17:21
Peano Arithmetic is a theory with equality, and $x = y\to Sx = Sy$ is one of the axioms of equality.
6 replies | 363 view(s)
• October 6th, 2019, 17:05
And this is not possible either (why?). Yes. For further practice, it is recommended proving that in an ordered field $-1<0$ and that your...
9 replies | 314 view(s)
• October 6th, 2019, 16:54
The book "Basic Set Theory" by A. Shen and N. K. Vereshchagin and this question from StackExchange say that the axiom of choice is needed to select a...
8 replies | 220 view(s)
• October 5th, 2019, 23:31
I am reading Theodore W. Gamelin's book: "Complex Analysis" ... I am focused on Chapter 1: The Complex Plane and Elementary Functions ... I am...
3 replies | 309 view(s)
• October 4th, 2019, 10:04
Thank you very much! My friend said that "worked like a charm." (Yes)
2 replies | 305 view(s)
• October 3rd, 2019, 21:48
Hello All! (Wave) A friend on another site reached out to me with a question regarding using Excel. I told him I know nothing about it, but that I...
2 replies | 305 view(s)
• October 3rd, 2019, 17:41
I don't see how it helps. In fact, I don't think a bijection can be continuous here.
8 replies | 220 view(s)
• October 3rd, 2019, 17:27
Find a correct axiomatization of an ordered field in a textbook or in Wikipedia. It is not given, but this is a separate problem. If we just want...
9 replies | 314 view(s)
• October 3rd, 2019, 14:48
I don't know much about the axiom of choice, but the goal is not to use it, but to prove the original claim. If in the construction one needs this...
8 replies | 220 view(s)
• October 3rd, 2019, 14:39
Then real numbers don't form an ordered field...
9 replies | 314 view(s)
• October 1st, 2019, 15:25
MarkFL replied to a thread [SOLVED] 274 7.2.6a int tan^4 x dx = in Calculus
I would write: I=\int \tan^2(x)(\sec^2(x)-1)\,dx=\int \tan^2(x)\sec^2(x)\,dx-\int \tan^2(x)\,dx The first integral is straightforward ad for...
3 replies | 721 view(s)
• September 30th, 2019, 15:32
Hello, and welcome to MHB! (Wave) I'm a self-diagnosed Aspie, but for me the experience has been that I stay ultra focused on the things in which...
2 replies | 1280 view(s)
• September 29th, 2019, 22:58
Oh! Indeed ... Cauchy-Riemann equations are only satisfied at (0,0) ... therefore the only possible point where the derivative of f can exist is...
2 replies | 268 view(s)
• September 29th, 2019, 14:03
The fact that $x\in A-B$ means that $x\in A$ and $x\notin B$. The negation of that, i.e., $x\notin A-B$, means that $x\notin A$ or $x\in B$. Thus,...
3 replies | 308 view(s)
• September 29th, 2019, 01:51
I am reading Tom M Apostol's book "Mathematical Analysis" (Second Edition) ... I am focused on Chapter 16: Cauchy's Theorem and the Residue...
2 replies | 268 view(s)
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