Fortress shipment

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No Flag Jaeger
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Re: Fortress shipment

Post by Jaeger »

pecelot wrote:indeed guys, forts are pretty situational, it's risky to put them in decks as they may turn out to be uneffective!

OUT!!
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Re: Fortress shipment

Post by Jaeger »

Jerom wrote: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 the 19th and early 20th centuries, there was a huge disaster in the field of mathematics. All the sloppy definitions and unjustified manipulations yielded paradoxes and came crashing down. Some ideas were totally thrown out the window, like Leibniz's infinitesimals, which do not exist in modern math (for the most part). Instead, they were replaced by limits, which involve only real numbers and have very precise definitions (https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit)

Out of the ashes came up a very strict and rigorous mathematics, which sought to avoid coming to such a disaster ever again.

If you set rules for yourself, you have to go where the rules lead you, even if it's not intuitive. Even in physics, if you only believe/accept what seems intuitive, you won't get very far. You just have to trust and follow the rules that you have set for yourself and the theorems you have proven. Yeah in physics the rules can be shown to be wrong sometimes since we can't really be sure they are true, but in math that never happens because we prove without a doubt the rules are true.

With that said, what I just said is not really true lol. Godel's Incompleteness Theorem (https://en.wikipedia.org/wiki/G%C3%B6de ... mpleteness) says that we can't ever be sure our math is right. I haven't studied this, but iirc any system of axioms powerful enough to describe the math we know cannot be proven self-consistent. That is, there might be contradictions laying deep in our mathematics; we could never prove we are free of contradictions. But anyway rigorous math is good.
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Re: Fortress shipment

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Jerom wrote: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.
Well, not exactly. Turns out there's a pretty good practical reason for why we can't divide by zero: Try distributing 10 cookies to 0 people, how many cookies is that per person?

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.
Division does work properly, it's just that you can't divide something into zero parts. This is obvious both in theoretical maths and in practice. x^3/x is indeed equal to x^2, except for x = 0. I don't like exceptions either, but I don't see the farce there.

I'm curious at this point, when has dividing by zero ever helped you get to a result where you otherwise couldn't? It seems to me that if that happened it would probably mean it helped you get to the wrong result.
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Re: Fortress shipment

Post by iNcog »

This thread got two more pages since yesterday evening. lol
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Re: Fortress shipment

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Post by BrookG »

iNcog wrote:This thread got two more pages since yesterday evening. lol

I even made a desperate maths thread... :hmm:
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Re: Fortress shipment

Post by Mr_Bramboy »

..fort?
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Re: Fortress shipment

Post by momuuu »

Goodspeed wrote:
Jerom wrote: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.
Well, not exactly. Turns out there's a pretty good practical reason for why we can't divide by zero: Try distributing 10 cookies to 0 people, how many cookies is that per person?

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.
Division does work properly, it's just that you can't divide something into zero parts. This is obvious both in theoretical maths and in practice. x^3/x is indeed equal to x^2, except for x = 0. I don't like exceptions either, but I don't see the farce there.

I'm curious at this point, when has dividing by zero ever helped you get to a result where you otherwise couldn't? It seems to me that if that happened it would probably mean it helped you get to the wrong result.

The inconsistency bothers me a lot actually. The 'solution' is to call it undefined, which is hardly a satisfying solution. Actually the case of needing x^3/x = x^2 is very common, and itd be pleasant if zero didnt constantly drop out.

Also Ive been thinking more about the implications of the limit and the more Ive been thinking about what it implies, the more this bothers me. If the limit exists it is literally screaming for it to actually be the value of the function in that place. You can get infinitely close to that point. That doesnt just mean infinitely close, youre also infinitely nothing away, which would be zero away from that point. You are at the point with infinite precision. Yet apperantly you are not. It is almost inconsistent in itself. Fortunately the limit is vaguely defined in the sense that using logic to concepts of infinite is hard, so its a less apperant problem but for me it is almost directly an inconsistency.
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Re: Fortress shipment

Post by Goodspeed »

There's no inconsistency there. You simply cannot divide something into zero parts, whether you're deep into trying to solve a complex problem or just trying to distribute 10 cookes to 0 people. You should stop pretending that dividing by zero is only impossible because it runs into contradictions in mathematics and admit that it also makes a lot of practical sense. Sure it may be convenient for you to allow division by zero (again, I'm really curious about how this was actually useful to you) but the fact that you keep implying that there is something wrong with maths for not allowing it is bothering me. These laws exist for a reason, as per usual in mathematics.
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Re: Fortress shipment

Post by momuuu »

It is at the very least an inperfection and it is extremely ugly aswell as impractical. It's almost inconsistent aswell with the limit, it kinda is but not really.
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Re: Fortress shipment

Post by Goodspeed »

The fact that it's not possible to divide something into zero parts is an imperfection in maths? Why exactly? I see no problem with it because practically it's just as impossible to divide by zero as it is in mathematics, which means maths is still able to perfectly describe real world situations.

There's no such thing as almost in maths. "Almost inconsistent" means nothing to me here.

Still eagerly waiting on that example
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Re: Fortress shipment

Post by Generator »

I think Jerom has finally figured out how to divide something by zero. He is on the right track to a Nobel Peace prize :P
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Re: Fortress shipment

Post by Goodspeed »

Yes, allowing division by zero is sure to bring about world peace. After all every computer in the world would crash, meaning we'll have bigger problems than waging war on each other :hmm:
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Re: Fortress shipment

Post by Goodspeed »

pecelot wrote:indeed guys, forts are pretty situational, it's risky to put them in decks as they may turn out to be uneffective!

Still not as ineffective as refrigeration and royal mint. People love those cards but it's totally undeserved, they are only viable in very long games which are rare and unpredictable which means you have to put the card in every deck just in case. The last time I sent either of these cards is when I was in a long fortress war and there were very little resources left on the map and it was my last fortress card. If I had colonial unit shipments left I would have sooner sent those, or better yet land grab.
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Re: Fortress shipment

Post by pecelot »

you may be right here, goatspeed! :hmm:
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Re: Fortress shipment

Post by momuuu »

Doesnt mean the fort shipment is better than crates or a unit shipment.
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Re: Fortress shipment

Post by momuuu »

Goodspeed wrote:The fact that it's not possible to divide something into zero parts is an imperfection in maths? Why exactly? I see no problem with it because practically it's just as impossible to divide by zero as it is in mathematics, which means maths is still able to perfectly describe real world situations.

There's no such thing as almost in maths. "Almost inconsistent" means nothing to me here.

Still eagerly waiting on that example

Because the limit of some functions implies strong that it is possible to divide zero by zero.
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Re: Fortress shipment

Post by Jaeger »

@Jerom
I can make a function:

g(x)=x^2 if x=/=2

And just leave it undefined at 2. Therefore the limit as x approaches 2 is 4, but g(2) is literarly undefined, because I haven't told you what happens at x=2. Asking what is g(2) is just as nonsensical as asking what is g(cow), because I never said anything about those input values. I, the maker of the function, could define g to be 5 at x=2, or to be 4 at x=2, or to be airplane at x=2. It's just undefined the way I left it.

Does this feel wrong too?
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Re: Fortress shipment

Post by Goodspeed »

Jerom wrote:
Goodspeed wrote:The fact that it's not possible to divide something into zero parts is an imperfection in maths? Why exactly? I see no problem with it because practically it's just as impossible to divide by zero as it is in mathematics, which means maths is still able to perfectly describe real world situations.

There's no such thing as almost in maths. "Almost inconsistent" means nothing to me here.

Still eagerly waiting on that example

Because the limit of some functions implies strong that it is possible to divide zero by zero.
So you are now saying you generally can't divide by zero but you can divide zero by zero?

I'm still not clear on your position apparently. Starting to wonder if you are
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Re: Fortress shipment

Post by momuuu »

My official position is that the limit of x/x is 1 and nothing less, but I like to go beyond that.

Unfortunately all you guys then say is that yo ucant divide by zero which is disappointing.

@ovi12 If you want to define it that way, then yeah it seems right, no idea why you'd do that though. I think convention where the existing limit is the value in a problematic point of a function would be more useful.
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Re: Fortress shipment

Post by gibson »

This should win the award for lamest thread of the year
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Re: Fortress shipment

Post by Goodspeed »

Jerom wrote:My official position is that the limit of x/x is 1 and nothing less, but I like to go beyond that.

Unfortunately all you guys then say is that yo ucant divide by zero which is disappointing.
To me the fact that you don't seem to understand the implications of what you're saying is disappointing. Your position is that "problematic points" in a function, which is to say whenever you divide by zero, should be assigned the value of that function's limit as x approaches that problematic point. Correct?

What this practically does is allow division by zero. By stating the above, you are saying that 1/0 = infinity, 0/0 = 1 etc. If you disagree with those statements then you are not being consistent.
(you are also saying everything equals everything but let's not get into that one)
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Re: Fortress shipment

Post by Generator »

Jerom wrote:My official position is that the limit of x/x is 1 and nothing less, but I like to go beyond that.

Unfortunately all you guys then say is that yo ucant divide by zero which is disappointing.

@ovi12 If you want to define it that way, then yeah it seems right, no idea why you'd do that though. I think convention where the existing limit is the value in a problematic point of a function would be more useful.

Calculator gave me error when I started to learn math and it is still giving me an error to this day when I divide by zero :(
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Re: Fortress shipment

Post by momuuu »

Goodspeed wrote:
Jerom wrote:My official position is that the limit of x/x is 1 and nothing less, but I like to go beyond that.

Unfortunately all you guys then say is that yo ucant divide by zero which is disappointing.
To me the fact that you don't seem to understand the implications of what you're saying is disappointing. Your position is that "problematic points" in a function, which is to say whenever you divide by zero, should be assigned the value of that function's limit as x approaches that problematic point. Correct?

What this practically does is allow division by zero. By stating the above, you are saying that 1/0 = infinity, 0/0 = 1 etc. If you disagree with those statements then you are not being consistent.
(you are also saying everything equals everything but let's not get into that one)

It practically does allow division by zero in the sense that you get the result it was supposed to be, which is great. 1/0 being infinity is actually a very practical result, but I spoke about existing limits. But what my suggestion would be is that in a function the limits automatically replace the point for the problematic values in a function. So if f(x) = x/x then f(0) would be defined. Its basically the inverse of having to define the missing points manually, rather if you want points excluded you have to define that like ovi did a few points up. Its in a sense just a notational suggestion that gives the function itself rather more consistency than less.
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Re: Fortress shipment

Post by pecelot »

Goodspeed wrote:
pecelot wrote:indeed guys, forts are pretty situational, it's risky to put them in decks as they may turn out to be uneffective!

Still not as ineffective as refrigeration and royal mint. People love those cards but it's totally undeserved, they are only viable in very long games which are rare and unpredictable which means you have to put the card in every deck just in case. The last time I sent either of these cards is when I was in a long fortress war and there were very little resources left on the map and it was my last fortress card. If I had colonial unit shipments left I would have sooner sent those, or better yet land grab.

Although to be fair, you gain a lot in the late game. It's pretty similar to factories ā€” you have to have them in your decks, despite the fact that you are able to send them in like 1/10 games. Had you not put them there, though, you'd be put on a major disadvantage, and the same applies to Royal Mint and Refrigeration IMO ā€” when the vill numbers are maxed out and you have around 35ā€”40 vills gathering both food and coin, it gives you a huge boost overall. It gets less significant when the game ends in the Imperial Age, as there are a lot of other upgrades and these two cards enlarge only the base gathering rates, but still I think it's a must in most cases. Sometimes, when I don't have too much space in the Fortress Age, I leave Refrigeration in and put the ā€žCigar Roller" card (age 2, 20%).
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Re: Fortress shipment

Post by BrookG »

pecelot wrote:
Goodspeed wrote:
pecelot wrote:indeed guys, forts are pretty situational, it's risky to put them in decks as they may turn out to be uneffective!

Still not as ineffective as refrigeration and royal mint. People love those cards but it's totally undeserved, they are only viable in very long games which are rare and unpredictable which means you have to put the card in every deck just in case. The last time I sent either of these cards is when I was in a long fortress war and there were very little resources left on the map and it was my last fortress card. If I had colonial unit shipments left I would have sooner sent those, or better yet land grab.

Although to be fair, you gain a lot in the late game. It's pretty similar to factories ā€” you have to have them in your decks, despite the fact that you are able to send them in like 1/10 games. Had you not put them there, though, you'd be put on a major disadvantage, and the same applies to Royal Mint and Refrigeration IMO ā€” when the vill numbers are maxed out and you have around 35ā€”40 vills gathering both food and coin, it gives you a huge boost overall. It gets less significant when the game ends in the Imperial Age, as there are a lot of other upgrades and these two cards enlarge only the base gathering rates, but still I think it's a must in most cases. Sometimes, when I don't have too much space in the Fortress Age, I leave Refrigeration in and put the ā€žCigar Roller" card (age 2, 20%).

It's probably better to have in 3v3 than 2v2, since you'd better have unit cards on the second case.
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