## Search found 215 matches

- Wed May 03, 2017 2:04 am UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

What is either program going to do without any arguments? Oracle tells us what a particular program does when given a particular input . It needs both of those arguments in order to do anything at all . Devious responds to what Oracle tells us the program corresponding to the one argument for Devio...

- Wed May 03, 2017 1:53 am UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Oracle is part of the Devious program. A program that takes an input and divides that input by three doesn't need three as an argument, because the three is always part of that program. Similarly, Devious checks what Oracle says about its input. It doesn't need Oracle as an argument, because Oracle...

- Wed May 03, 2017 1:50 am UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

After having proved that the formula is valid for all n, you can replace n with k+1. If you do that, you get sum to k+1 = (k+1)(k+2)/2 At which step do I "prove[ ] that the formula is valid for all n"? I'm confused by that statement. Please - can someone tell me directly what comes after ...

- Wed May 03, 2017 1:47 am UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Oracle is already part of Devious, by definition. As in, that's how we defined Devious. How can Devious make Oracle do anything if Devious isn't taking Oracle as an argument? If arguments don't matter, then why do we go to pains to emphasize that Oracle takes two arguments, one of which is a progra...

- Wed May 03, 2017 1:38 am UTC
- Forum: Coding
- Topic: Basic Question Involving Functions (Python)
- Replies:
**14** - Views:
**1625**

### Re: Basic Question Involving Functions (Python)

Since you're a total beginner, I recommend steering away from most Python tutorials; they'll generally be teaching you Python itself, and assume you already have basic knowledge of how programming itself works. There's a big list of Python-related "I'm totally new to this whole programming non...

- Wed May 03, 2017 1:37 am UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

gmalivuk wrote:Devious takes one argument, but to get the contradiction, the argument it takes is (the number corresponding to) Devious itself, not Oracle.

OK. So Devious takes only one argument (a program, Devious). How does Oracle get into the picture if Devious takes only one argument?

- Wed May 03, 2017 12:25 am UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Almost! There's one part where I'm unclear what you're referring to, so let's clear that up: Here, we design a world in which we have Devious call Oracle as its sole argument. It sounds like you're saying here that Devious takes Oracle as its sole argument. Is this what you meant? If so, then this ...

- Tue May 02, 2017 11:58 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

Unfortunately, the algebra steps are (mostly) too small to be legible Do you mean conceptually? :P Because you can click the image for a full resolution version that you can read ...and you can click the full resolution image again to zoom it to actual scale, assuming you don't have an expensive ul...

- Tue May 02, 2017 11:48 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

I dunno. Here's the steps again: * The Devious machine is large, and contains an Oracle machine inside of itself. * The Devious machine expects to be fed a box of parts. It'll then either explode, or print a smiley face. * It does this by feeding that box of parts to its internal Oracle machine. * ...

- Tue May 02, 2017 11:46 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

If you want to continue down the even-or-odd induction proof path, then please (for my sanity) explain, using the contents and steps of that even-or-odd proof, how each piece of content and each step from that proof relates to if/then statements and the steps of the original induction proof that I'...

- Tue May 02, 2017 11:15 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

I'm going back to machines, because otherwise I don't understand how to suss out the issues. Oracle is already built into Devious; it's one of Devious's sub-components. Devious takes a box of parts as its input, magically duplicates the box, then passes both boxes to Oracle. The "trick" t...

- Tue May 02, 2017 11:07 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Almost! There's one part where I'm unclear what you're referring to, so let's clear that up: Here, we design a world in which we have Devious call Oracle as its sole argument. It sounds like you're saying here that Devious takes Oracle as its sole argument. Is this what you meant? If so, then this ...

- Tue May 02, 2017 10:59 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

There is not. You can write the proof a different way, in which you use substitution INSTEAD of adding to both sides. But since you're talking about step 2, where you have already added to both sides, you are definitely not using that way. OK. Then what do I need to do to get from Step 2 to Step 3?

- Tue May 02, 2017 10:57 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Let me discard the physical objects example and explain what I've got so far: Oracle is supposed to tell us whether a given program with a certain input will halt or not. And Oracle is also supposed to itself halt (i.e., Oracle must return an answer of "halt" or "won't halt"). Or...

- Tue May 02, 2017 10:53 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

Meteoric wrote:There is no substitution step. We add stuff to both sides, rearrange, and that's it.

No, I'm certain that there's a substitution step - others have referenced it in this thread.

- Tue May 02, 2017 10:47 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Xanthir wrote:Devious takes one box of parts. It then magically duplicates that box, inside itself, for its own internal reasons.

But you only *gave* it one box. It takes one argument, not two.

Then I don't understand. Is Oracle involved in the duplication?

- Tue May 02, 2017 10:46 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

I will be happy to give such a step-by-step when I am back at a real keyboard, but that will have to wait a few hours. The reason I am avoiding your question about step 2 is that, last time, we spent a full page on the same question, concluding with you saying "I give up". We explained an...

- Tue May 02, 2017 10:42 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Xanthir wrote:I'm quoting parts of my previous post that answer this exact issue. What part of those quotes are confusing you?

I don't understand the duplication of parts by Devious and how that doesn't mean that Devious doesn't take two arguments.

- Tue May 02, 2017 10:37 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Yeah. What's the relevance of that? It does this by feeding that box of parts to its internal Oracle machine. * But the Oracle machine needs two inputs, as we already established. So the Devious machine first *duplicates* the box of parts you gave it, then feeds both of those boxes to the Oracle. T...

- Tue May 02, 2017 10:34 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

No, it only takes one. Why would you think that it needs to take two? * The Devious machine expects to be fed a box of parts. It'll then either explode, or print a smiley face. * It does this by feeding that box of parts to its internal Oracle machine. * But the Oracle machine needs two inputs, as ...

- Tue May 02, 2017 10:30 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

INDUCTION STEP: Assume that k is either even or odd. If k is even, then k+1 is odd. If k is odd, then k+1 is even. So either way, k+1 is either even or odd. I assumed k is either even or odd, then used it to prove that k+1 is. That's how you say I should prove "If n is either even or odd, then...

- Tue May 02, 2017 10:24 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

I don't understand the contains-an-Oracle-machine inside itself part (recall that before Oracle accepted only two arguments), We've hit this point before - it's like your phone containing smaller machines in it - a CPU, a screen, a speaker, etc. The Oracle is a piece inside the large Devious machin...

- Tue May 02, 2017 10:17 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Okay. So now we can finally move the Devious machine. Tell me where this stops making sense: * The Devious machine is large, and contains an Oracle machine inside of itself. * The Devious machine expects to be fed a box of parts. It'll then either explode, or print a smiley face. * It does this by ...

- Tue May 02, 2017 10:15 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

But you don't seem to know how to prove them, which is what we're doing here. We keep circling around this same problem. The induction step is just a conditional proof. If I demonstrate that a base case is true, and then demonstrate that if the k case is true then the (k + 1) case is true, then I'v...

- Tue May 02, 2017 10:13 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

It's because your original goal, in all of this induction, is to prove that there is a nice, simple formula for finding the sum of the first n positive integers. That formula is n(n+1)/2. You're trying to prove this is true for all positive integers, right? k is just a positive integer. k+1 is just...

- Tue May 02, 2017 10:09 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

Meteoric wrote:Isn't that what I did above?

I don't see that.

- Tue May 02, 2017 10:06 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Yeah. We do distinguish the two, *right now*, and that's important - the Oracle doesn't *actually* feed the example input to a machine, because that might explode it; it just analyzes the box of parts, and tells you whether it would explode if it were constructed and fed the example input. Awesome....

- Tue May 02, 2017 9:56 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

Meteoric wrote:And how do you prove if-then statements? Like, can you prove "If n is even then n^2 is a multiple of 4"?

You would assume that "n is even" is true, and then show that if that assumption is true, then the "n^2 is a multiple of 4" part must also be true.

- Tue May 02, 2017 9:48 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Like I said, it doesn't matter. (I answered that way because I assume a machine that lights things on fire would contain some flammable material, perhaps a propane tank, and this would explode when fed to a running LightsThingsOnFire machine.) Can we distinguish between machines and boxes containin...

- Tue May 02, 2017 9:38 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

Xanthir wrote:What's confusing about the fourth example that's not confusing about the third example? The two are, intentionally, almost identical.

I don't see why the fourth result should be BOOM.

- Tue May 02, 2017 9:34 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

But you don't seem to know how to prove them, which is what we're doing here. We keep circling around this same problem. The induction step is just a conditional proof. If I demonstrate that a base case is true, and then demonstrate that if the k case is true then the (k + 1) case is true, then I'v...

- Tue May 02, 2017 9:31 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

↶ Yes, although to keep me less confused can we keep the two arguments consistent (i.e., machine and loose parts)? Maybe. I'm reluctant to do this because you're talking about the first argument as a "machine", which sounds like you're meaning a fully-assembled one. This confusion between...

- Tue May 02, 2017 9:28 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

You're struggling here for the same reason I've noted before: you don't seem to understand the difference between a conditional and its parts. You CANNOT understand induction without first understanding conditionals. They're what induction is made of. I can draft truth tables to test conditionals. ...

- Tue May 02, 2017 9:09 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

I don't know how that counts as an induction proof. I've established only two alternatives, and not a single answer. In other words, there are two rungs and I haven't told anyone which rung we're actually on. We are assuming that the 'current' rung is either even or odd. And we want to prove that t...

- Tue May 02, 2017 9:06 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

↶ ↶ Why do the machine and the input need to be separate? How about just giving the Oracle a machine and asking whether it'll blow up or not? Because A machine's behavior can change based on what you feed it, tho - some inputs make it explode, others don't. OK. That makes sense. So we're passing bo...

- Tue May 02, 2017 8:55 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

That IS the proof. Suppose I claimed that, somewhere out past six billion, there is a number that is neither even (a multiple of 2) nor odd (a multiple of 2, plus 1). This proof by induction shows that isn't true: the number before it is either even or odd, so my number is either odd or even. I don...

- Tue May 02, 2017 8:54 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

We can design Oracle to take one input, but it still has to interpret this input as a program together with input for that program. For example, we could have a different oracle that takes input 72 (which is 2 2 *3 2 ) and tells us what program 2 does with input "2", but it's still answer...

- Tue May 02, 2017 8:52 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

↶ Why do the machine and the input need to be separate? How about just giving the Oracle a machine and asking whether it'll blow up or not? Because A machine's behavior can change based on what you feed it, tho - some inputs make it explode, others don't. OK. That makes sense. So we're passing both...

- Tue May 02, 2017 8:51 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**252** - Views:
**2556**

### Re: Mathematical Induction - Introductory Question

I don't know how that counts as an induction proof. I've established only two alternatives, and not a single answer. In other words, there are two rungs and I haven't told anyone which rung we're actually on. The rungs in induction are always the natural numbers. Even/odd are not rungs. You've prov...

- Tue May 02, 2017 8:48 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**200** - Views:
**3174**

### Re: Halting Problem

At some point I have to believe that you're either trolling, or you have serious memory problems on top of math difficulties. The first input to Oracle is the number of a program. The second input to Oracle is the input we give that program. Oracle(4,5) tells us what program number 4 does when it r...