Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 Re: Puzzles and Games » Phi Brain (Anime) Puzzle » 2016-04-11 07:16:03

Also, because of country issues, I'm not sure, but here is another link you can use.  The youtube one cuts off for me at the top and bottom, plus, while youtube is free and legal, the person putting the video up isn't always.  There are no issues with watching these, but you can expect them to quite frequently get taken down.

## #2 Re: Puzzles and Games » Phi Brain (Anime) Puzzle » 2016-04-10 13:33:35

Hmmm, I guess I should post my own answers (again, they aren't absolutely correct, only what I think).

Also, I apologize about not posting my own answers earlier, I forgot about the whole hiding answers, then I was searching the forum, because I couldn't figure out what the tag was.  Of course it would be the one thing I wasn't thinking...  [ hide ] and [ / hide ] (without the spaces).

In case anyone is interested in my answers for the actual phi brain puzzle in episode two (usually around 6:30 - 7:00 in the episode; you can find at http://www.crunchyroll.com/phi-brain/ep … ard-595519 where it is free and legal if you don't mind ads):

## #3 Re: Puzzles and Games » The Achilles diary paradox » 2016-04-10 12:36:38

Relentless wrote:

I think Solvitur means the paradox that an immortal being can do all of:
1. Make a promise
2. Never fulfill that promise, and
3. Never break that promise either.

Tis one of many fun things playing around with anything infinite can get you.

## #4 Re: This is Cool » Fun with 0 / 0 » 2016-03-26 09:10:03

Oh yeah, I realize 0/0 is also used for that purpose with convenience.  One of the things that actually gets me interested in these kinds of things is seeing how it may potentially be something other than what you think it is when you look more at it.  So in arithmetic, you learn 0 / 0 = (undefined), but then you begin to think, wait a second, what does that even mean exactly?  Why is it even undefined?  You learn more math later on, as you move on to algebra, calculus, um...set theory, also things you just simply study on your own, etc., which may provide you with even more reasoning for why it is like that.  But then, my friend tells me of something like this he concocts, and then, you just kind of laugh and say, this is seemingly quite simple and appears to make sense while also finding it quite clever (well I do anyway).  Even if it isn't true and doesn't work, I find the whole thing very interesting and still wonder if it does work with more explanation.  It still think on some level it could fit in, but there's so much I don't know, I'm not even able to say that with confidence.

## #5 Re: Puzzles and Games » The Achilles diary paradox » 2016-03-26 08:59:10

What is it you mean more specifically when you say the 'permanent postponement paradox' and how is that related?  Like I guess I'm asking, is that explaining how this whole paradox works, or... (Sorry, I guess I'm asking for more details as I'm just not very sure what you mean).

## #7 Re: Puzzles and Games » Phi Brain (Anime) Puzzle » 2016-03-26 07:15:27

I apologize, I've been busy in school and as a result haven't gone on for quite a while.  I'm not entirely sure if any of you are asking a question for more information, telling me you think I did something wrong with the puzzle or maybe just having a discussion amongst yourselves.  I guess to clarify, on Episode 2 of Phi Brain (first season), they show this puzzle (I think around 5 min. in), which if I recall correctly, is the second puzzle.  The issue is I personally wanted to see if what I had was correct, yet they never showed the answer.  So I tried to replicate the same puzzle to see what answers others got as maybe my own answers are incorrect.  I mean, if they don't give an answer, who's really to say who is right or wrong, could be better decided by others.

Now it's possible that when trying to make my own puzzle based on theirs, I messed something up.  However, based on the patterns I saw in the set-up, I didn't see any issue.  One notable difference is in the original puzzle, there were 3 boxes left w/o answers (and 2 of them used letters which can be assumed you had to figure out what A and B were equal to unless I'm mistaken).  In mine, I only had 2 blank ones which was meant to be very identical to how they did it in their puzzle (which like the video, I put in 2 letters left to be figured out).  I can put down what I think the answers are, but I still wanted to see what others thought of it too (without influencing their answers).  I did not make up this puzzle, therefore, my own personal "answers" may not be correct.

*EDIT*  I fixed grammar mistakes and played around with what edit looks best.

## #8 Puzzles and Games » Is this an impossible question? » 2016-01-09 12:48:01

Calligar
Replies: 8

A while ago, I was talking to someone on Omegle.  For those who aren't familiar, Omegle is a website where you can video or text chat anonymously (unless you reveal who you are) with a random person online.  One of the things they gave me was what they called an "Impossible Question", but supposedly actually has an answer.  If I recall correctly, the question goes something like this...

I pick a random number from 1 to 100.  Of the four numbers I list, which one did I pick?

A. 71
B. 81
C. 83
D. 90

I never was told what the answer was, but I'm curious what other people would choose (for those who even choose an answer).

## #9 Re: This is Cool » Fun with 0 / 0 » 2016-01-09 12:46:28

0^0 = 1 is actually quite interesting.  It seems to go against what one would think.  Let's see, how does the one proof go again...?  1 = A^n/A^n = A^(n-n) = A^0...something like that...

Oh, rofl, I see!  0^0/0^0.  I was just about to post and caught that .

## #10 Re: Puzzles and Games » The Achilles diary paradox » 2016-01-09 12:26:37

Relentless wrote:

Calligar,

Hahaha, you have basically made a duplicate of the first paragraph of post #3 Post #4 is a good response to this query - in short, you (and I) are right!

Lol, sorry about that.  I read everything, but since it took me longer to understand everything, so I guess I figured that out after you and forgot you said anything about that.

Solvitur ambulando wrote:

I have now revised the Diary Paradox to avoid the 'Paradox of Permanent Postponement'. The former hinges on the ordering of infinite series whereas the latter highlights the potential pitfalls of conceptualising infinite time.

Lol, interesting how you specifically wanted to avoid what Relentless and I found .

## #11 Re: This is Cool » Fun with 0 / 0 » 2016-01-09 12:13:14

Okay, I just want to make sure you have caught this...

Calligar wrote:

Anyway, let me make my case clear now, 0/0 ≠ v.  It was an interesting comparison, comparing the answer to a variable, but it just isn't as simple as that.  I am still interested in what people have to comment on it because I still find the comparison really interesting as it reminds me of something a kid would do.  But I want to make sure everyone understands I don't actually think this is how it works...

Basically, all this time, I wasn't trying to prove it, unless I was making arguments for the fun of it, which aren't entirely correct.  I was merely trying to explain that there was an interesting comparison my friend made.  The logic (and possibly one of the flaws too) is that when dealing with multiplication, division is the opposite.  Therefore, whatever you multiply, you can turn around to divide.  So 4×2 = 8 and 2×4=8.  So, 8÷2 = 4 and 8÷4 = 2.  Using that logic, comes the 0÷0, the problem is.  Since v×0 = 0 and 0×v = 0, then 0÷0 = v and 0÷v = 0.  We already know that 0 divided by anything = 0 (unlike anything divided by 0), therefore, there will be less argument against that.  The problem is saying 0÷0, as you start running into more issues.

Now another one of the issues with what I did, which is pretty much wrong, was with this example:

Calligar wrote:

0÷0+b = a-1
0÷0+b+1 = a
0(0÷0+b+1) = 0(a)
0[(0÷0)+(+b+1)] = 0(a)
0(0÷0)+0(b+1) = 0(a)
0+0(b+1) = 0(a)
*0(b+1) = 0(a)

filling in 3 for b....
0(3+1) = 0(a)
0(4) = 0(a)
0 = 0

Let me do something quick that will make it seem wrong.
2 ≠ 3
0(2) ≠ 0(3)
0 ≠ 0

Talking to my friend recently about this, he will still argue it's correct, actually making the argument both 0s are not equal.  In the example he gave, he would have taken it further and reversed the whole thing as well.  He also would not have done the last thing I did where I said 0 = 0.  So I think that's the end of me trying to make arguments for his case .  Now here...

zetafunc wrote:

You've mentioned "going deeper" with this -- could you elaborate?

I may have given a brief example of taking it a little deeper, but to be honest, I am not really sure I want to go too much deeper into that (at least at this time), because that's beginning to go into things that don't exist (at least within my knowledge) and also complicated things that already exist, expanding on rules or changing other ones.  And I'm not even the one that came up with it, making it more difficult to explain something my own friend did (which is frustrating especially when I make certain mistakes).  I'd prefer to not use things like 0÷0 at all as other than just working on the math of it as I don't really have any use for that (so just going into the pure math for the fun of it I guess).

The reason I brought it up here is not to argue what this said is correct, just a curious example that may get you to think about it some more (especially those who aren't familiar with why 0÷0 is undetermined).  I know a few years ago (I think I even brought it up on this forum), I honestly thought 0÷0 = only 0.  Knowing that 1÷0 = undefined, but specifically was wondering why that was the case with 0÷0.  I figured it out later, but when I talked to my friend about it, and he had this whole thing set up for it already that used pretty much basic algebra to try to show it.  I thought it was a very curious example, wrong or not.  Basically, I was curious about other peoples reactions to that, because I honestly thought it was pretty cool the first time I saw it (even if I don't really believe that to be the case).

Also, I'm not ignoring all the cases you gave zetafunc, I'm honestly still looking into those.  The wheel theory I find pretty interesting.  But I don't know how much further I can actually answer your questions to be honest, at least at this time.  Also, I'm not familiar enough with some of the things your saying.  For instance, I'm honestly not sure what you mean each time you're using ∈ nor am I the most familiar with set theory (which I have done very little work with; better just to say I don't know set theory), though I believe I understand the rest of it (could be mistaken).

Note:  Also saying 0÷0 = v = ℝ probably is fine, though, I'm unsure if my friend would put it the same way as I'm not sure if he would restrict it to only real numbers or possible include even more.

## #12 Re: Puzzles and Games » The Achilles diary paradox » 2016-01-05 21:30:19

Hmm, okay, I see you edited your original post, I got the information I needed.  Though I am curious about one thing.  Why did he have to take any non-birthday pages.  Since he lives forever, he could take birthday pages and only birthday pages for eternity.  I understand the part that he must eventually take all the pages, but with no time limit, that is actually irrelevant unless I'm mistaken.  I would argue that since he is living forever and can choose what pages (out of unlimited pages) to take out, he should be able to take arguably only birthday pages because he can theoretically always take all his non-birthday pages later (of course, that later will never happen).

## #13 Re: This is Cool » Fun with 0 / 0 » 2016-01-05 21:10:56

zetafunc wrote:

In other words, you start by assuming that 0/0 is undefined? I'm still having trouble understanding precisely what you mean: are we simply replacing "0/0" with "v", here? If not, can you give a more precise definition of v?

Here, let me make this easier; let's start off like this.
0×0 = 0, 1×0 = 0, 2×0 = 0, 3×0 = 0, etc..  Therefore, instead of listing the unlimited different answers, one just simply puts the variable "v".  So it looks like this: v×0 = 0.  Therefore, this reasoning looks at it in a way that if it were v×0=0, then 0÷0 = v.  The issue is, with this, you can not define "v" or it won't work.  If you were to say 0÷0 = 1, then 0÷0 ≠ 2.  That is why it remains "v" and stays undefined.  However, I personally don't see this as a solution either, and going deeper with this has its difficulties to say the least.

Another thing I wanted to clarify:

Relentless wrote:

For example, you mentioned that the answer to 1/0 could be infinity.

I apologize if I left that impression.  I'll make try to make this clear now.  I do not believe 1/0 = ∞.  Not even close actually.  Not only do you have an issue of using infinity as a number, but it just won't work, at least not that simply.  Like I left in my earlier example, if 1/0 = ∞, then what is 2/0 = ?.  Logically, one would start to conclude 2/0 = 2∞, however when dealing with infinity, that doesn't seem to make sense.  Putting this in this simple form, when you divide 1 by 0, what number do you get?  When you divide 2 by 0, what number do you get?  Surely you don't get the same number for both problems, do you?  Infinity is also not a number.  And while it can at times be used similarly to one, it doesn't mean it is one.  That's at least how I like to think about it (putting it simply).

## #14 Re: This is Cool » Fun with 0 / 0 » 2016-01-02 13:09:21

Okay, just for fun.  Let's say that what my friend said is true (which I'm not saying it is).  In that example, v (or any variable), and not just any number would have to be equal to 0 / 0.  What you are trying to do is get to the answer 0 / 0.  As it stands, if you were to multiply 0 by any number, you would get 0.  Therefore, using that, 0 / 0 does not make 1, nor 2, nor 3.  It remains an undefined variable unless you were using it in some defined manner.

Now how can the variable possible be defined.  So I'll make up a problem to try to give an example.  So the problem would go something like this:  0÷0+b = a-1.  If b is 3, show that 0(a) = 0(4).
0÷0+b = a-1
0÷0+b+1 = a
0(0÷0+b+1) = 0(a)
0[(0÷0)+(+b+1)] = 0(a)
0(0÷0)+0(b+1) = 0(a)
0+0(b+1) = 0(a)
*0(b+1) = 0(a)

filling in 3 for b....
0(3+1) = 0(a)
0(4) = 0(a)
0 = 0

Now after doing all that, my point arises with the specific variable being defined, while 0÷0 still existing.  0÷0 still however remains undefined in this way.  That's the first part of what I was talking about...

Calligar wrote:

1 ≠ 0/0, nor does 2.  v = 0/0, and it will remain undefined unless there's something else that will allow it to be defined.  In other words, v may = 1, v may = 2, but unless it is defined, you can't simply say it is 2.

The second part...

However, if v = 0/0, and for some reason v were defined as 3 in this case.  Then only 3 = 0/0, and not 2.  It would have to be specific to that 0/0.

Making this very simple, if 0/0 = v, and v = 3, then 0/0 = 3.  0/0 = v, but it also = 4, or 5, or 6.  Since v is now defined, v is just 1 of infinite things 0/0 may be.  Yet if you use an undefined variable, like in the example I gave where "a" never gets defined (but "v" does).  Even in step 2 where 0÷0+b+1 = "a", that's as much of a definition as you're going to get because you still can't determine what 0÷0 is, making a an even different undefined variable showing how this all may seem simple, but it can very quickly get more complicated.  So I repeat again, there's reason this remains undefined.  Comparing it to a variable is something interesting, but if you actually want to go deeper in understanding it, it will get more and more difficult as you advance.

I would also like to add that I made a bit of a mistake, saying "only 3 = 0/0, and not 2", like what I was saying above, is it's specific to the variable "v".  If 3 is defined as "v", then v ≠ 2, and 0/0 = um...let's say "w" which remains undefined, unless you define that as well, then you must use another variable as long as it remains undefined.

Anyway, let me make my case clear now, 0/0 ≠ v.  It was an interesting comparison, comparing the answer to a variable, but it just isn't as simple as that.  I am still interested in what people have to comment on it because I still find the comparison really interesting as it reminds me of something a kid would do.  But I want to make sure everyone understands I don't actually think this is how it works...

* *edit* I changed "v" to "b" because I noticed I put "v" by mistake....

## #15 Puzzles and Games » Phi Brain (Anime) Puzzle » 2016-01-02 11:00:25

Calligar
Replies: 10

During episode 2 of Phi Brain (an anime), they show a particularly puzzle which they don't give an answer to.  It seems like a relatively simple puzzle, I was just curious about other people's answers.  So in order to avoid any copyright issues, I made my own puzzle based on Phi Brain's puzzle.
Basically, find what A and B are equal to, or in other words...

A =
B =

*edit*  I fixed the mistake.

## #16 Re: Maths Is Fun - Suggestions and Comments » Chatroom » 2016-01-02 10:03:15

Interesting, I'll do some investigating into this then.  Because I do believe there is a way to get it to work still.  Such as, as I stated earlier, applying the chat room to say only members only areas and such; someplace that guests would not have access to it.

## #17 Re: Maths Is Fun - Suggestions and Comments » Chatroom » 2016-01-02 09:49:52

Interesting would you mind if I asked what those laws were, or some link to what they are?

## #18 Re: This is Cool » Fun with 0 / 0 » 2016-01-02 09:38:21

That's what Relentless also pointed out...

Relentless wrote:

One of the fundamental issues with dividing by zero is that if you allow it, then just as you get 1*0=0, 3.9425*0=0, you also get 1 = 3.9425

It is an issue with how you are looking at it.  If I were to try to argue the case, I'd say it's a bit flawed.  1 ≠ 0/0, nor does 2.  v = 0/0, and it will remain undefined unless there's something else that will allow it to be defined.  In other words, v may = 1, v may = 2, but unless it is defined, you can't simply say it is 2.  However, if v = 0/0, and for some reason v were defined as 3 in this case.  Then only 3 = 0/0, and not 2.  It would have to be specific to that 0/0.  However, please don't try to look at it this way.  Anything divided by 0 is undefined or the like, and for reason.  I'm not trying to argue that 0 / 0 should equal v.  I only was pointing out something interesting that helps you look at 0 / 0 that I found interesting (which doesn't mean it is correct).

## #19 Re: Dark Discussions at Cafe Infinity » What is Certain Knowledge? » 2016-01-02 09:24:51

To answer the first question (

What kinds of truths, in all seriousness, do you think are absolutely impervious to doubt?

), I'll put a very simple answer, rather than the lengthy one I was going to put.  What if I believed 1 + 1 = 4 instead of 2?  This knowledge is wrong, though perhaps it is because I'm misunderstanding something, or maybe I'm right in a different sense where I count using numbers differently.  However, to make this simple, let's just assume I'm wrong and it is just 1 + 1 = 2.  One can still be certain he is right, even though he is wrong.  He may actually believe that, and he himself may have no doubts, no matter how many people say he is wrong.  Therefore, to answer the question at the beginning, I can argue that 1 + 1 = 4 is a truth absolutely impervious to doubt, and continue to do so with lots of other examples.

Now for the second question (

The question is, what is left?

), which is very dependent on these events.  An answer I can also give for this, your own ability to think.

Interesting thing to answer, I'm curious what other people's responses are.

## #20 Re: Puzzles and Games » The Achilles diary paradox » 2016-01-02 08:18:28

Yes, sorry, I understood most of that.  The issue I'm having is some smaller details mentioned which is causing me to get confused about the whole thing.  It is why I quoted both of them:

Solvitur ambulando wrote:

As compensation for the error the gods allow him to tear out the pages of the diary in any order he chooses, each page determining his fate for the day.

For the first 364 days he tears out the pages corresponding to his first 364 birthdays

Those are the parts I'm having the most difficulty understanding.  However, you bring up now another question, which is related to trying to understand the first part I quoted (sorry about all the confusion, I'm only trying to understand this)...

Relentless wrote:

The idea is that tearing a page out represents choosing that day next.

So does that mean that by tearing a page out, it happens the day after?

## #21 Re: Maths Is Fun - Suggestions and Comments » Chatroom » 2016-01-02 07:55:44

No, I don't believe I have.  What is SOSA and PIPA?

## #22 Re: This is Cool » Fun with 0 / 0 » 2016-01-02 07:35:59

Relentless wrote:

One of the fundamental issues with dividing by zero is that if you allow it, then just as you get 1*0=0, 3.9425*0=0, you also get 1 = 3.9425

Interesting point (it took me a little bit to realize what you were saying).  It is at least one of the issues calling it v.  But again, I never listed it saying it was correct, I just thought that such a simple thing like that was worth mentioning out of interest.

Relentless wrote:

Personally, I think rather than saying that x/0 is equal to some undefined variable v, it is best to say that it is a question that does not make sense. When you think about 20 divided by 5, you are thinking about how many times you subtract 5 from 20 to get 0. So how many times do you subtract 0 from 1 to get 0? Well, you never will. How many times do you subtract 0 from 0 to get 0? As many as you like. They are really nonsense questions from that perspective.

Unfortunately dividing any other number by 0 creates a lot more issues.  I've worked with it before with my friend.  1 / 0 can not equal v like 0 / 0 can.  That point I made only works with 0 / 0.  As you pointed out, if you divide 1 / 0, you can not reach a number.  There isn't a number in existence (that I'm aware of) that can answer that question.  Some may argue the answer is ∞.  But then comes an issue with using ∞ as a number, which it isn't (or at least not exactly in that way).  Plus there are issues to that.  If say 1 / 0 = ∞, what does 2 / 0 = ?  Does it also equal ∞, does it equal 2∞?  How do you even begin to make sense of it?  You can make sense of it, but I don't know anything in mathematics that will answer it except for maybe...1 / 0 = undefined (or something of that nature).  Probably already realized all this, but at least interesting to point out.

## #23 Re: Help Me ! » 9999999 = 1 » 2016-01-02 07:20:15

No sorry, was not suggesting multiple threads nor did I realize this was the open thread, I thought this was supposed to be only for the (infinity)x thing and that seemed pretty much answered since I didn't see anymore counter arguments to it.  Saying it was open afterwards caused me to ask about it.

## #24 Re: Maths Is Fun - Suggestions and Comments » 0.9... = 1; Is it gone? » 2016-01-02 07:17:02

Okay, is that http://www.mathisfunforum.com/viewtopic.php?id=20534? Or is that a different one?  I was suggesting bringing back the big one to have a big one available, but I guess it doesn't matter if there is still one open.

## #25 Re: Maths Is Fun - Suggestions and Comments » Chatroom » 2016-01-02 06:55:54

What are the reasons if you don't mind me asking?