Fortress shipment
Re: Fortress shipment
I think crazy is the word here. x/x where x = 0 is the same as 0/0. Similarly, x + x = y where x = 2 can be written as 2 + 2 = 4.
Something something variables?
Something something variables?
Re: Fortress shipment
The road to the solution matters in my head. In a sense, I'd like to call the limit the real value, as that is everything the limit implies if it were to exist. As someone who likes to see maths as a tool rather than a science, this proposal is not problematic at all. For if the real world exhibits behaviour where the value infinitely close to one point is vastly different from the value at that point then I'd rather doubt my maths than this assumption. In a sense division by zero is in my eyes a mathematical failure and a mathematical problem, for those that apply maths it does not have to be a problem at all for as much as one can assume the limit is the value.
Re: Fortress shipment
ovi12 wrote:Jerom wrote:But nobody said that 0/0 is 1 jesus christ. If thats all you ahve to say then I'm just going to quit..
You are just contradicting youself, if you say 0/0 is undefined but (0*0*0)/0 =1. You have to pick one or the other. If you pick it's undefined, then x^3/x does not equal x^2 for all x, and you just have to accept that. Can't have it both ways
Actually, I didnt say 0*0*0/0 =1, I said 0*0*0/0 = 0*0 = 0. Hmm, it seems I trust you to much and assumed you quoted and interpreted me incorrectly. In a sense, I would like to believe x³/x is exactly x² for all points. In that sense, I'd like to claim x-49/(sqrt(x)-7) is exactly the same as sqrt(x)+7. That does not seem to cause a problem to me necessarily, to be entirely honest.
For example, x=x is compatible with x/x=1 for all values of x if you assume that x/x -> 0/0 is equal to one. It proposes a more elegant maths imo, unless you'd be able to provide a case where the limit really is off.
Re: Fortress shipment
So what you're saying is that, putting some of the laws of mathematics aside, you see no problem with the statement 0/0 = 1 because lim x->0 x/x = 1 and you see no practical reason why a statement like 0/0 shouldn't be equal to its limit?Jerom wrote:The road to the solution matters in my head. In a sense, I'd like to call the limit the real value, as that is everything the limit implies if it were to exist. As someone who likes to see maths as a tool rather than a science, this proposal is not problematic at all. For if the real world exhibits behaviour where the value infinitely close to one point is vastly different from the value at that point then I'd rather doubt my maths than this assumption. In a sense division by zero is in my eyes a mathematical failure and a mathematical problem, for those that apply maths it does not have to be a problem at all for as much as one can assume the limit is the value.
Re: Fortress shipment
I believe youre shortening my statement by omitting crucial parts of it, altering the content of the statement. Ive gone over it again and theres two primary thoughts that propel me:
- If the limit of a function exists in a problematic point, then the value of that limit may aswell be taken as the value for the function in that problematic point without any problems outside the world of mathematics
- The function x/x cannot be told apart from the function 1, just like how x³/x cannot be told apart from the function x². They are the same in my eyes.
I'm more so convinced of the former than the latter, but believe that in even the slightest case of application these two statements hold true.
- If the limit of a function exists in a problematic point, then the value of that limit may aswell be taken as the value for the function in that problematic point without any problems outside the world of mathematics
- The function x/x cannot be told apart from the function 1, just like how x³/x cannot be told apart from the function x². They are the same in my eyes.
I'm more so convinced of the former than the latter, but believe that in even the slightest case of application these two statements hold true.
Re: Fortress shipment
Isn't that what I said though?
What did I leave out in your opinion?
What did I leave out in your opinion?
Re: Fortress shipment
When talking about limits its very important to keep in mind where you came from, what function you are referring to, which makes the statement 0/0=1 an incorrect one and not in line with my proposed assumptions. After all that one creates more of a problem because it's inconsistent with the entire theorema proposed in the first place. It's exactly what needs to be omitted for any of it to hold true.
Re: Fortress shipment
Then you don't agree with your own statement.
Limit as x approaches zero: 1
Value for x = 0 according to your proposed assumption: 1
Hence 0/0 = 1
Disagree anywhere?
Function: x/x- If the limit of a function exists in a problematic point, then the value of that limit may aswell be taken as the value for the function in that problematic point without any problems outside the world of mathematics
Limit as x approaches zero: 1
Value for x = 0 according to your proposed assumption: 1
Hence 0/0 = 1
Disagree anywhere?
Re: Fortress shipment
Im not gonna respond to this yet since im on my phone but the example with the pencil illustrates that a limit and an actual value. Just because its manufactured to show this, and doesnt take into account many real world variables, doesnt mean that it doesnt prove in principle that taking the limit and evaluating the function at that value can give different results
last time i cryed was because i stood on Lego
Re: Fortress shipment
Goodspeed wrote:Then you don't agree with your own statement.Function: x/x- If the limit of a function exists in a problematic point, then the value of that limit may aswell be taken as the value for the function in that problematic point without any problems outside the world of mathematics
Limit as x approaches zero: 1
Value for x = 0 according to your proposed assumption: 1
Hence 0/0 = 1
Disagree anywhere?
Yes the last step.
Re: Fortress shipment
ovi12 wrote:Im not gonna respond to this yet since im on my phone but the example with the pencil illustrates that a limit and an actual value. Just because its manufactured to show this, and doesnt take into account many real world variables, doesnt mean that it doesnt prove in principle that taking the limit and evaluating the function at that value can give different results
For otherwise continuous functions aswell?
Re: Fortress shipment
Okay so
x/x where x = 0 is not the same as 0/0 in your eyes?
x/x where x = 0 is not the same as 0/0 in your eyes?
Re: Fortress shipment
In a sense no, x/x where x = 0 would then be defined by the limit of x->0 of x/x, rather than by 0/0 itself, since that is one of the problematic scenarios for said function. It's according to my first theorem right?
Re: Fortress shipment
Then for everyone's sanity include that in your function's definition
Re: Fortress shipment
Also,
I'm extremely curious as to why you added the "* x/x" here. Ironically the only reason to add something like this would be to make sure the function is undefined for x = 0, the addition serves no other purpose since it evaluates to "* 1" in every other case.Jerom wrote:zoom wrote:60/40 as Dutch?
12/9 * x/x is about good for dutch, so yes.
Re: Fortress shipment
You copypasta ovi. Much plagiarism.
But yes, basically that I guess. Except that I'd prefer to introduce it as a rule for all problematic functions for which such a limit exists so that you'd not have to write that gibberish and can use your time on solving actual problems instead.
Btw, part of my saltyness so to say is that this is the part of mathematics that annoys me a lot. Yes sure, some people care about that and find it really interesting, like ovi does and other mathematicians. I do not, I just want to know how I can safely apply maths to my fucking problems. I don't want to have to bother about these boundary conditions as much as I have had to. The maths Ive gotten have always been obscured by these irrelevant sidenotes to the degree that I've usually not been able to reach understanding until after I had applied the taught maths to practical problems in actual physics subjects. It's all nice that there's people that bother about some details which are mostly insignificant, and really when I fall over such a detail I will come to a mathematician and beg him to help me, but please let's not bother the rest of the world with them. It's not constructive or helpful in any sense and just confuses people. Maybe this is a prime example of it, where it made everyone miss a glaring mistake in what I wrote down much larger than some consideration of the case of zero villagers.
But yes, basically that I guess. Except that I'd prefer to introduce it as a rule for all problematic functions for which such a limit exists so that you'd not have to write that gibberish and can use your time on solving actual problems instead.
Btw, part of my saltyness so to say is that this is the part of mathematics that annoys me a lot. Yes sure, some people care about that and find it really interesting, like ovi does and other mathematicians. I do not, I just want to know how I can safely apply maths to my fucking problems. I don't want to have to bother about these boundary conditions as much as I have had to. The maths Ive gotten have always been obscured by these irrelevant sidenotes to the degree that I've usually not been able to reach understanding until after I had applied the taught maths to practical problems in actual physics subjects. It's all nice that there's people that bother about some details which are mostly insignificant, and really when I fall over such a detail I will come to a mathematician and beg him to help me, but please let's not bother the rest of the world with them. It's not constructive or helpful in any sense and just confuses people. Maybe this is a prime example of it, where it made everyone miss a glaring mistake in what I wrote down much larger than some consideration of the case of zero villagers.
Re: Fortress shipment
Goodspeed wrote:Also,I'm extremely curious as to why you added the "* x/x" here. Ironically the only reason to add something like this would be to make sure the function is undefined for x = 0, the addition serves no other purpose since it evaluates to "* 1" in every other case.Jerom wrote:zoom wrote:60/40 as Dutch?
12/9 * x/x is about good for dutch, so yes.
So that you could get the direct villager allocations as a function of the amount of villagers you have. Problem is that I didnt take banks into account like a proper scrub.
Re: Fortress shipment
Actually in that light 0/0 is a very desired result.
Re: Fortress shipment
Jerom wrote:Goodspeed wrote:Also,I'm extremely curious as to why you added the "* x/x" here. Ironically the only reason to add something like this would be to make sure the function is undefined for x = 0, the addition serves no other purpose since it evaluates to "* 1" in every other case.Show hidden quotes
So that you could get the direct villager allocations as a function of the amount of villagers you have. Problem is that I didnt take banks into account like a proper scrub.
What is x? the amount of villagers? "* x/x" still doesn't make any sense.
If you want a 4:3 allocation and you have x villagers you need 4/7x vills on the one resource and 3/7x on the other. Or, have it your way, 12/21x and 9/21x.
Re: Fortress shipment
Yes he already wrote it down so why notJerom wrote:You copypasta ovi. Much plagiarism.
Well you can't because you run into mathematical fallacies, as ovi and I demonstrated. What you are saying is that you want to make a general rule that allows division by zero, and to assign the value of the limit when doing so. 1/0 would equal infinity, for example. It would also equal -infinity, which is another fallacy but let's not get into that. The key seems to be producing a practical example where your proposal breaks down and I'm sure there is one, but I'm no physicist so I'm afraid I can't help there. You are correct about the pencil example being horse shit, I'll give you that.But yes, basically that I guess. Except that I'd prefer to introduce it as a rule for all problematic functions for which such a limit exists so that you'd not have to write that gibberish and can use your time on solving actual problems instead.
You'll be careful though? A physicist who ignores mathematical fallacies because they are inconvenient seems somehow scary to me. I guess I can take comfort in the fact that a physicist like that would probably not be taken very seriously.Btw, part of my saltyness so to say is that this is the part of mathematics that annoys me a lot. Yes sure, some people care about that and find it really interesting, like ovi does and other mathematicians. I do not, I just want to know how I can safely apply maths to my fucking problems. I don't want to have to bother about these boundary conditions as much as I have had to. The maths Ive gotten have always been obscured by these irrelevant sidenotes to the degree that I've usually not been able to reach understanding until after I had applied the taught maths to practical problems in actual physics subjects. It's all nice that there's people that bother about some details which are mostly insignificant, and really when I fall over such a detail I will come to a mathematician and beg him to help me, but please let's not bother the rest of the world with them. It's not constructive or helpful in any sense and just confuses people. Maybe this is a prime example of it, where it made everyone miss a glaring mistake in what I wrote down much larger than some consideration of the case of zero villagers.
Re: Fortress shipment
I wont be a groundbreaking physicist anyways lol, Im not in that tier. Oh, did you know that Planck might a crucial mathematical error in one of his theories that wasnt discovered until much later by Einstein, or that Einstein himself greatly struggled with the mathematics required for general relativity. He contacted a mathematician about it and evidence suggests that mathematician could at that point have written down his entire theory in a verh short time, while Einstein struggled with it for years. Also, Einstein missed the most obvious and easiest solution to his equations, a spherically symmetric one, that is now known as a black hole. Theres still hope martspeed.
About the practical example existing: Im actually doubtful for the reason that the limit in practical sense defines the value. For you approximate the value in that point so infinitely well that the limit actually goes to that value. That means, being zero away from the said point produces the value of the limit.
About the practical example existing: Im actually doubtful for the reason that the limit in practical sense defines the value. For you approximate the value in that point so infinitely well that the limit actually goes to that value. That means, being zero away from the said point produces the value of the limit.
Re: Fortress shipment
Goodspeed wrote:Jerom wrote:Show hidden quotes
So that you could get the direct villager allocations as a function of the amount of villagers you have. Problem is that I didnt take banks into account like a proper scrub.
What is x? the amount of villagers? "* x/x" still doesn't make any sense.
If you want a 4:3 allocation and you have x villagers you need 4/7x vills on the one resource and 3/7x on the other. Or, have it your way, 12/21x and 9/21x.
Yes, x would be the amount of villagers divided by 21. I was just having some innocent fun writing something down but apperantly I fucked up by practically dividing by zero.
Re: Fortress shipment
@Jerom
You're totally fine if you write functions like this, but you can't say that f(c)=g(c). There is no theorem here, you haven't proved anything. The best you can hope for is to establish a convention that we just assume that we assign the limiting value to a function at a discontinuity, but this would be counterproductive and confusing since you won't be really writing down what you mean when you write (sin x)/x for example
Jerom wrote:notification
You're totally fine if you write functions like this, but you can't say that f(c)=g(c). There is no theorem here, you haven't proved anything. The best you can hope for is to establish a convention that we just assume that we assign the limiting value to a function at a discontinuity, but this would be counterproductive and confusing since you won't be really writing down what you mean when you write (sin x)/x for example
last time i cryed was because i stood on Lego
Re: Fortress shipment
What I dont really get is that the limit almost enforces that statement, or at least enforces that assumption. After all you approach the problematic point infinitely closely. In other words, your basically zero away from it. The only reason not to call it that is because of a mathematical formalism, because itd interfere with other algebraic rules. That is why I feel relatively comfortable claiming that there is no real scenario in which an existing limit gives an inappropriate solution for a problematic point of a function.
In a sense division is the farce of mathematics, because it doesnt always work properly. The idea that x^3/x isnt equal to x^2 is the most counter intuitive thing ever and honestly a small failure of our mathematical formalism. Good thing the Jeromapproach is generally applied to that scenario, aswell as the x/x scenario.
In a sense division is the farce of mathematics, because it doesnt always work properly. The idea that x^3/x isnt equal to x^2 is the most counter intuitive thing ever and honestly a small failure of our mathematical formalism. Good thing the Jeromapproach is generally applied to that scenario, aswell as the x/x scenario.
Re: Fortress shipment
indeed guys, forts are pretty situational, it's risky to put them in decks as they may turn out to be uneffective!
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