Fortress shipment

[momuuu]

Also, I believe I saw somewhere that even if the top of the pencil is 1 atom diameter off of pi/2, the pencil will only take 3 seconds to fall. If you actually figure out the formula and show that as you get arbitrarily close to pi/2 then the time for the pencil to fall approaches infinity, then yeah it would debunk my example. But I'm not sure if this is the case. It's possible that as theta approaches pi/2, the time just approaches 5s for example.

A quick google search confirms that this is the case for even smaller values than that, but we are talking about a limit here and Jerom is right in saying that there are values extremely close to 90 degrees where the pencil takes longer than a minute to fall. If there weren't, I think we would have bigger issues than the limit not being zero.
I guess your physics guy mentioned this example because it's known to be counter intuitive how quickly the pencil falls even when almost upright, but it doesn't quite hold up.

Anyway

Im saying the limit of x->0 for x/x is defined precisely as 1

This seems blatantly obvious. It's always 1, except of course for x = 0.

@Jerom

notification

You should probably drop your hate of mathematics if you want to be a physicist worth a damn. To me it seems obvious that a thorough understanding of mathematical concepts is one of the most important skills to have as a physicist.

On topic, I actually like the fort shipment in most of my decks. It's situational, but not half as situational as the eco upgrades (royal mint, refrigeration) which should probably not be in anyone's 1v1 deck at all.

I hate maths in that they always bitfuck over things like this. But I believe that we reach a very terrible situation if x/x is not defined for x=0.

[Jaeger]

But then x^2 in 0 is not defined. 0/0 on its own is not necessarily defined in my eyes. I just believe x/x and x^3/x to be defined in zero. They have to be by laws of division.

Again read what I am saying.

But can you explain to me how saying that (0*0*0)/0 =defined but 0/0=not defined is not contradictory? f(x)=x^3/x is a different function from g(x)=x^2. f happens to coincide with g, but only when x is in (-infinity, 0)U(0, infinity).

Maybe you will remember from your math classes. Remember before calculus, when they were giving us problems like (x^2+2x+1)/((x+1)(x+2)) and they were asking to find the domain and vertical asymptotes? We would simplify (x^2+2x+1)/((x+1)(x+2)) to (x+1)/(x+2)), and say there is a vertical asymptote at x=-2, and that there is a hole at x=-1. And when we graphed it, there was always a hole. And when we would give the final result, we would give:

(x+1)/(x+2), domain : (- infinity, --2U(-2, -1)U(-1, infinity)

[Goodspeed]

Also, I believe I saw somewhere that even if the top of the pencil is 1 atom diameter off of pi/2, the pencil will only take 3 seconds to fall. If you actually figure out the formula and show that as you get arbitrarily close to pi/2 then the time for the pencil to fall approaches infinity, then yeah it would debunk my example. But I'm not sure if this is the case. It's possible that as theta approaches pi/2, the time just approaches 5s for example.

A quick google search confirms that this is the case for even smaller values than that, but we are talking about a limit here and Jerom is right in saying that there are values extremely close to 90 degrees where the pencil takes longer than a minute to fall. If there weren't, I think we would have bigger issues than the limit not being zero.
I guess your physics guy mentioned this example because it's known to be counter intuitive how quickly the pencil falls even when almost upright, but it doesn't quite hold up.

Anyway

Im saying the limit of x->0 for x/x is defined precisely as 1

This seems blatantly obvious. It's always 1, except of course for x = 0.

@Jerom

notification

You should probably drop your hate of mathematics if you want to be a physicist worth a damn. To me it seems obvious that a thorough understanding of mathematical concepts is one of the most important skills to have as a physicist.

On topic, I actually like the fort shipment in most of my decks. It's situational, but not half as situational as the eco upgrades (royal mint, refrigeration) which should probably not be in anyone's 1v1 deck at all.

I hate maths in that they always bitfuck over things like this. But I believe that we reach a very terrible situation if x/x is not defined for x=0.

Then I guess we are in a terrible situation. 0/0 is absolutely undefined, are you seriously arguing against that? Because from your previous statements I thought I gathered that you were only arguing lim x -> 0 x/x = 1.
Careful, or you will talk yourself into holes you can't get out of. There's no ambiguity in maths.

[Mr_Bramboy]

So how about this fort thing, guys?

[Goodspeed]

Pretty good card, 7/10 would put in deck over royal mint

[forgrin]

The fort itself is fine for its purpose. Because it builds very slowly though you can easily lose it if your opponent is paying attention.

[Goodspeed]

I like it in early fortress, if you camp on it with your army then your opponent has to choose between sieging it down (which is not easy with small armies, especially skirm+goon armies) and lose a ton of units to your army or let it go up. People often choose to try and siege it down and lose way too much, it's excellent bait

[Jaeger]

The fort itself is fine for its purpose. Because it builds very slowly though you can easily lose it if your opponent is paying attention.

Wtf why u hijack this math thread with random fort talk?

[forgrin]

The fort itself is fine for its purpose. Because it builds very slowly though you can easily lose it if your opponent is paying attention.

Wtf why u hijack this math thread with random fort talk?

The original math issue arose talking about vill allocations, specifically 12/9 * x/x. If you have 0 vills then you collect 0 resources, not undefined or 1.

Sometimes maths and physics people need bio people for context :p

[momuuu]

The fort itself is fine for its purpose. Because it builds very slowly though you can easily lose it if your opponent is paying attention.

Wtf why u hijack this math thread with random fort talk?

The original math issue arose talking about vill allocations, specifically 12/9 * x/x. If you have 0 vills then you collect 0 resources, not undefined or 1.

Sometimes maths and physics people need bio people for context :p

x here is a representation of the amount of vills and how that'd affect the allocation. Very wrong btw because it doesnt scale like that due to banks, but nobody minds that for some reason.

[Jaeger]

The fort itself is fine for its purpose. Because it builds very slowly though you can easily lose it if your opponent is paying attention.

Wtf why u hijack this math thread with random fort talk?

The original math issue arose talking about vill allocations, specifically 12/9 * x/x. If you have 0 vills then you collect 0 resources, not undefined or 1.

Sometimes maths and physics people need bio people for context :p

Nope, whatever units x has, they cancel out in x/x. And because x=x, you have 12 vills/12 vills, or 4 resources/4 resources, you don't have resources/vill. The units just cancel anyway and it's just a scalar of 1

[Jaeger]

Also, I believe I saw somewhere that even if the top of the pencil is 1 atom diameter off of pi/2, the pencil will only take 3 seconds to fall. If you actually figure out the formula and show that as you get arbitrarily close to pi/2 then the time for the pencil to fall approaches infinity, then yeah it would debunk my example. But I'm not sure if this is the case. It's possible that as theta approaches pi/2, the time just approaches 5s for example.

A quick google search confirms that this is the case for even smaller values than that, but we are talking about a limit here and Jerom is right in saying that there are values extremely close to 90 degrees where the pencil takes longer than a minute to fall. If there weren't, I think we would have bigger issues than the limit not being zero.
I guess your physics guy mentioned this example because it's known to be counter intuitive how quickly the pencil falls even when almost upright, but it doesn't quite hold up.

Anyway

Im saying the limit of x->0 for x/x is defined precisely as 1

This seems blatantly obvious. It's always 1, except of course for x = 0.

@Jerom

notification

You should probably drop your hate of mathematics if you want to be a physicist worth a damn. To me it seems obvious that a thorough understanding of mathematical concepts is one of the most important skills to have as a physicist.

On topic, I actually like the fort shipment in most of my decks. It's situational, but not half as situational as the eco upgrades (royal mint, refrigeration) which should probably not be in anyone's 1v1 deck at all.

I hate maths in that they always bitfuck over things like this. But I believe that we reach a very terrible situation if x/x is not defined for x=0.

Why would we reach a terrible situation?
Also, people have been careful to make life easy for you and themselves, for example by defining the sinc (x) function

[momuuu]

I like to believe x³/x = x²
I guess its hard to come up with great problems for someone that doesnt care that much but I feel like its better to just assume this to be true. Its much easier at the very least.

[Akechi_Mitsuhide]

actually not only 0/0 is undefined. you cant divide by zero at all.

[Jaeger]

I like to believe x³/x = x²
I guess its hard to come up with great problems for someone that doesnt care that much but I feel like its better to just assume this to be true. Its much easier at the very least.

But assuming that gives you much bigger problems (not that x^3/x =/= x^2 is actually a problem)

This is from my post to Kaiser

[momuuu]

But nobody said that 0/0 is 1 jesus christ. If thats all you ahve to say then I'm just going to quit..

[Jaeger]

I like to believe x³/x = x²
I guess its hard to come up with great problems for someone that doesnt care that much but I feel like its better to just assume this to be true. Its much easier at the very least.

Also I think you have a problem because these 3 functions would look weird, they approach something other than 1 as x->0, then they jump to 1

[Jaeger]

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

[momuuu]

Im not saying that I just claim that a function like x/x is defined in zero....

[Jaeger]

Im not saying that I just claim that a function like x/x is defined in zero....

[momuuu]

So at the problematic point the value is equal to the limit, which you denied earlier? If you need to write that down so formally that is absolutely fine with me, but I'll for most of my life and hopefully all of it assume that the value at a problematic point is equal to the limit if it converges and is continuous so to say.

In other words, f(x) = x/x then f(0) = 1 is absolutely and completely satisfactory to me, which has always been my position.

[Jaeger]

So at the problematic point the value is equal to the limit, which you denied earlier? If you need to write that down so formally that is absolutely fine with me, but I'll for most of my life and hopefully all of it assume that the value at a problematic point is equal to the limit if it converges and is continuous so to say.

In other words, f(x) = x/x then f(0) = 1 is absolutely and completely satisfactory to me, which has always been my position.

Well it will not be the function x/x which equals 1 at zero, it will be a different function, g. This function agrees with x/x for all x not equal to 0, and deviates from x/x at 0 because x/x is not defined at 0, while g will be defined (as 1, or 2, or pi, or whatever you want). What might not sit right with you is that it would not be incorrect to define g(0) as something other than 1. Everything is fine if we talk about g, it's continuous (if you chose g(0)=1). But when we talk about x/x, then that's not continuous. That's one of the reasons why they made the sinc function, so that you don't have to say x =/= 0 when you talk about (sinx)/ x

[momuuu]

I am absolutely and completely fine with calling the limit the actual value and only see mathematical concerns arise from it which can easily be ignored. I guess I chose the easy road in life and went with a practical point of view. Call it a mistake, but I hope I can call it a succesful decision in the future.

It is besides a position most of us hold in practical use of mathematics. Theres many cases in derriving formulas where a division is made and two entities are there for removed from the equation for being of the form x/x, where almost nobody actually bothers about redefining the function for 0 so be equal to the limit. Once you remove that you can act like nothing ever happened. In other words, x³/x = x² except for ovi and his mathematical brothers in crime.

[Goodspeed]

But nobody said that 0/0 is 1 jesus christ. If thats all you ahve to say then I'm just going to quit..

f(x) = x/x then f(0) = 1

???

Are you saying there's a difference between "is" and "=" or what's going on here?

[momuuu]

But nobody said that 0/0 is 1 jesus christ. If thats all you ahve to say then I'm just going to quit..

f(x) = x/x then f(0) = 1

???

Are you saying there's a difference between "is" and "=" or what's going on here?

I see two distinctly different things there, but maybe Im just crazy or ahead of the meta.