Fortress shipment

[iNcog]

who the fuck thinks that 0/0 = 1

the rule that you cannot divide by 0 is stronger than the rule that dividing something by itself gives you 1

duh..

[momuuu]

who the fuck thinks that 0/0 = 1

the rule that you cannot divide by 0 is stronger than the rule that dividing something by itself gives you 1

duh..

0*infinite should be 0 right?

Its about the limit of a function, and for the sake of having functional mathematics assuming the problematic point is equal to its limit is extremely pleasant and practically the correct thing to do.

[iNcog]

yeah 0 is stronger than infinity, but only when doing multiplications!!!1

[Jaeger]

who the fuck thinks that 0/0 = 1

the rule that you cannot divide by 0 is stronger than the rule that dividing something by itself gives you 1

duh..

Jerom wasn't reading for the second time I guess while critizing me for not reading. Kaiser said, among others:

"Doesn't need to since it's x/x. The result will be 1 whatever the value of x is, even if it's 0"

"No it doesn't. The limit of x/x is 1 when x -> 0- and it's also 1 when x -> 0+. So, since the limit is continuous, you deduce that x/x has a limit of 1 when x -> 0. In other words, you can write 0/0 = 1."

"so sin(0)/0 = 1. Same when you do 0/0 since x~sin(x) when x->0."

He is clearly saying that 0/0=1. Not that we can approximate it to be 1 in physics problems. He is saying that mathematically 0/0=1.

The objection to calling f(0) of f(x)=x/x is purely mathematical. Its a mathematical failure to begin with, and taking the limit and calling that the value solves the mathematical failure to the extend that everyone, including reality, but a mathematician is satisfied.

Its what aiz implied to, and kaiser did aswell

It's not what aiz implied imo, but if you read my quotes the third time I mention them, you will see that kaiser claimed that 0/0=1 is valid mathematically, not just that it makes sense in physics.

0*infinite should be 0 right?

Its about the limit of a function, and for the sake of having functional mathematics assuming the problematic point is equal to its limit is extremely pleasant and practically the correct thing to do.

[iNcog]

I'm joking, for the record.

Rules can't be "stronger" than other rules in math. It's either true or false. lol

[Jaeger]

@Jerom

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And let me guess, you probably think that "multiplying" both sides by a differential such as dx, or "cancelling out the dx" is ok too. Because that one is easily false even in physics

[Jaeger]

@Jerom

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I had to actually talk to a REAL physicist ( ) and he gave me examples of real world functions which give you wrong results if you assume their value at some point is equal to the limit value

[momuuu]

Does not seem logical by everything that the limit implies.

[Jaeger]

Does not seem logical by everything that the limit implies.

Would be nice to quote me like I always quote you you know so I don't have to dig for this thread every time

The example he gave me is this:

Balance a pencil on a flat table. You can put the table at any angle theta between 0 and pi/2, with 0 being flat on the table, and pi/2 being completely vertical. Let f(theta) be the angle at which the pencil is 1 minute later. This way, the limit as theta approaches pi/2 of f(theta) is 0, but f(pi/2) itself is pi/2, so you would get the wrong answer if you assumed that the limit is equal to the value.

This is not quite a 0/0 case but it shows you that the limit isn't always equal to the function value, even in real life situations

[momuuu]

your example makes little sense tbh, what even are you taking the limit of and what is the limit going towards..
@ovi12

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lazy piece of shit read threads more freq1uently I hate quotes.

[BrookG]

@Jerom

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@ovi12

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viewtopic.php?f=26&t=6912

[Jaeger]

your example makes little sense tbh, what even are you taking the limit of and what is the limit going towards..
@ovi12

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lazy piece of shit read threads more freq1uently I hate quotes.

Then you can tag me like you did. You are taking the limit of f(theta) as theta approaches pi/2, where theta is the initial angle you set the pencil to, and f(theta) is the angle at which the pencil is 1 after 1 minute after when you let go of the pencil.

The limit as f(theta) as x approaches pi/2 is 0, because the pencil will take less than 1 minute to fall for any theta<pi/2. So if we assume the function is continuous (because according to you all real world functions are continuous) then we should assume that f(pi/2)=0, because lim as theta approaches pi/2 = 0. But f(pi/2) is actually pi/2, because the pencil never falls

[momuuu]

I have two things to say. First of all, your example is pure shit. If you actually just do the maths and compose the formulas to calculate the time then theres no limit that you have to take lol, and above all, there will be miniscule angles extremely close to pi/2 which will give a value for f(theta) larger than 0. So please tell that grand physicists to go get a real degree kthxbye

Secondly, you're just completely wrong about the x/x case. You got confused by mathematicianness and lost common sense, unfortunately all of us to some degree lost the touch with thinking a little bit too, except for our god aizamk. By your exact logic, x^2 is undefined in 0. So is x, or any function in the world. The flaw is that we assume x/x is any different than 1, which it is not by the basic rules of division. If it was not exactly equal to one, then maths crash. In that case
x³/x =/= x². A division of something by itself is 1, that's how it is defined. In other words calculating the limit would be done as following: f(x)=x/x=1. Lim x->0 [1] = 1 which is very much a real value.

In other words, Kaiser is the most right in this thread after all, but was sidetracked by being overly complex. Also, you getting upset because I multiplied by x/x because I didnt define x=/=0 is unjustified, as I literally multiplied by something defined as one.

@ovi12

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[Jaeger]

I have two things to say. First of all, your example is pure shit. If you actually just do the maths and compose the formulas to calculate the time then theres no limit that you have to take lol, and above all, there will be miniscule angles extremely close to pi/2 which will give a value for f(theta) larger than 0. So please tell that grand physicists to go get a real degree kthxbye

I really don't see the problem with this example. It's a function that describes the real world. Yes, you can go into more detail and calculate the angle the pencil makes with the table, but thats not the point. The point is:
1) Does this function describe reality? Yes
2) Is this function continuous? No

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.

Secondly, you're just completely wrong about the x/x case. You got confused by mathematicianness and lost common sense, unfortunately all of us to some degree lost the touch with thinking a little bit too, except for our god aizamk. By your exact logic, x^2 is undefined in 0. So is x, or any function in the world. The flaw is that we assume x/x is any different than 1, which it is not by the basic rules of division. If it was not exactly equal to one, then maths crash. In that case
x³/x =/= x². A division of something by itself is 1, that's how it is defined. In other words calculating the limit would be done as following: f(x)=x/x=1. Lim x->0 [1] = 1 which is very much a real value.

In other words, Kaiser is the most right in this thread after all, but was sidetracked by being overly complex. Also, you getting upset because I multiplied by x/x because I didnt define x=/=0 is unjustified, as I literally multiplied by something defined as one.

Before I respond to this, do you admit to believing that 0/0=1?

[momuuu]

I have two things to say. First of all, your example is pure shit. If you actually just do the maths and compose the formulas to calculate the time then theres no limit that you have to take lol, and above all, there will be miniscule angles extremely close to pi/2 which will give a value for f(theta) larger than 0. So please tell that grand physicists to go get a real degree kthxbye

I really don't see the problem with this example. It's a function that describes the real world. Yes, you can go into more detail and calculate the angle the pencil makes with the table, but thats not the point. The point is:
1) Does this function describe reality? Yes
2) Is this function continuous? No

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.

Secondly, you're just completely wrong about the x/x case. You got confused by mathematicianness and lost common sense, unfortunately all of us to some degree lost the touch with thinking a little bit too, except for our god aizamk. By your exact logic, x^2 is undefined in 0. So is x, or any function in the world. The flaw is that we assume x/x is any different than 1, which it is not by the basic rules of division. If it was not exactly equal to one, then maths crash. In that case
x³/x =/= x². A division of something by itself is 1, that's how it is defined. In other words calculating the limit would be done as following: f(x)=x/x=1. Lim x->0 [1] = 1 which is very much a real value.

In other words, Kaiser is the most right in this thread after all, but was sidetracked by being overly complex. Also, you getting upset because I multiplied by x/x because I didnt define x=/=0 is unjustified, as I literally multiplied by something defined as one.

Before I respond to this, do admit to believing that 0/0=1?

a) Then its not a continuous function to begin with, as only discrete input values are allowed. Realistically thermal pressure would eliminate deviations from perfectly straight and not cause the pencil to fall, or push the pencil out of equilibrium. In other words this is a shitty approximation and therefor taking the limit of it is a shitty thing to do to begin with. If we assume a perfect mathematical standing pencil then the limit works out and this guy fucked up his physics and maths.
b) I didnt say that. Read again.

[Jaeger]

a) You can input values anywhere on the interval [0, pi/2], so you're not limited to plugging in discrete values. f(pi/6)=f(pi/123)=f(49pi/100)=0. f(pi/2)=pi/2. Yes were assuming a perfect pencil, but all of physics is just a simplified model of reality. This just happens to be a model that is simplified a lot.

b) Yes I read like 3 times. My only claim is that 0/0 is not defined, nothing less, nothing more. But you said I am completely wrong, so I don't know how else to interpret what you said.

It seems like on one hand you are trying to say 0/0 is technically undefined. But then you are saying that on some level 0/0 MUST be 1 because x^3/x=x^2. The reality is that x^3/x equals x^2 if and only if x =/= 0. I can elaborate more on this, but first you need to clarify if I am interpreting your position correctly.

[momuuu]

Im saying the limit of x->0 for x/x is defined precisely as 1, which you contradicted.

[Jaeger]

Im saying the limit of x->0 for x/x is defined precisely as 1, which you contradicted.

Nope, I totally agree that the limit as x->0 of x/x=1. Can you show me where I said the opposite?

Also, do you agree that x^3/x=x^2 if and only if x=/=0?

[momuuu]

a) You can input values anywhere on the interval [0, pi/2], so you're not limited to plugging in discrete values. f(pi/6)=f(pi/123)=f(49pi/100)=1. f(pi/2)=pi/2. Yes were assuming a perfect pencil, but all of physics is just a simplified model of reality. This just happens to be a model that is simplified a lot.

In the case that you can input values anywhere then the formula that you'd derrive to calculate this (something you probably didnt even ask for to see given your posts) then the limit is actually equal to the real value for the formula imposed on the problem. What abotu this do you not get?

[momuuu]

Im saying the limit of x->0 for x/x is defined precisely as 1, which you contradicted.

Nope, I totally agree that the limit as x->0 of x/x=1. Can you show me where I said the opposite?

Also, do you agree that x^3/x=x^2 if and only if x=/=0?

I do not, I believe it is the same regardless. After all, x^3=x^3 for x=0 so that works out perfectly. If it was not the same for x=0 then x^3 isnt equal to x^3 clearly

[Jaeger]

Im saying the limit of x->0 for x/x is defined precisely as 1, which you contradicted.

Nope, I totally agree that the limit as x->0 of x/x=1. Can you show me where I said the opposite?

Also, do you agree that x^3/x=x^2 if and only if x=/=0?

I do not, I believe it is the same regardless. After all, x^3=x^3 for x=0 so that works out perfectly. If it was not the same for x=0 then x^3 isnt equal to x^3 clearly

How can you hold the belief that (0*0*0)/0 is defined, while holding the belief that 0/0 is undefined? These are just contradictory positions because (0*0*0)/0 = 0/0

[momuuu]

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.

[Jaeger]

a) You can input values anywhere on the interval [0, pi/2], so you're not limited to plugging in discrete values. f(pi/6)=f(pi/123)=f(49pi/100)=1. f(pi/2)=pi/2. Yes were assuming a perfect pencil, but all of physics is just a simplified model of reality. This just happens to be a model that is simplified a lot.

In the case that you can input values anywhere then the formula that you'd derrive to calculate this (something you probably didnt even ask for to see given your posts) then the limit is actually equal to the real value for the formula imposed on the problem. What abotu this do you not get?

First, I made a type, I meant to say f(pi/6)=f(pi/123)=f(49pi/100)=0

I think you misunderstood the function, f(theta) takes as input the starting angleof the pencil, and gives the angle of the pencil after 1 minute. Then every pencil that was not started at pi/2 will be horizontal on the table (unless it is the case that a pencil at for example .999999999999999999999999999999999 of pi/2 takes longer to fall than a minute (or any finite time) but I doubt this is the case)

[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 you 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

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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.

[momuuu]

a) You can input values anywhere on the interval [0, pi/2], so you're not limited to plugging in discrete values. f(pi/6)=f(pi/123)=f(49pi/100)=1. f(pi/2)=pi/2. Yes were assuming a perfect pencil, but all of physics is just a simplified model of reality. This just happens to be a model that is simplified a lot.

In the case that you can input values anywhere then the formula that you'd derrive to calculate this (something you probably didnt even ask for to see given your posts) then the limit is actually equal to the real value for the formula imposed on the problem. What abotu this do you not get?

First, I made a type, I meant to say f(pi/6)=f(pi/123)=f(49pi/100)=0

I think you misunderstood the function, f(theta) takes as input the starting angleof the pencil, and gives the angle of the pencil after 1 minute. Then every pencil that was not started at pi/2 will be horizontal on the table (unless it is the case that a pencil at for example .999999999999999999999999999999999 of pi/2 takes longer to fall than a minute (or any finite time) but I doubt this is the case)

Yes and that exact case solves your problem. Its 0 for a lot of values of theta, then slowly spikes up to pi/2 from EXTREMELY small angles. You don't have to doubt this is the case, you have to do the logic or maths and figure out that it is the case. And this is why this example is besides pure and absolute shit also extremely untrue. Its a bad show, first you simplify and example and leave things out for some weird purpose, and then you apply very exact mathematics to something that isnt even a function but just an assumption. Is this guy a "real physicists"? Because that'd be embarassing for me.