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### AuthorTopic: Maximum Possible VP?  (Read 6694 times)

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#### werothegreat

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##### Re: Maximum Possible VP?
« Reply #25 on: November 21, 2017, 11:01:12 am »
+1

Play 5 Highways then Goons. Have Trader in hand. Buy Forum forever, gain an arbitrary amount of VP.
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##### Re: Maximum Possible VP?
« Reply #26 on: November 21, 2017, 11:19:26 am »
+5

[...] gain an arbitrary amount of VP.
π is pretty arbitrary, as are -1, i, φ, e, sqrt(2) and Chaitin's constant
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#### Cave-o-sapien

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##### Re: Maximum Possible VP?
« Reply #27 on: November 21, 2017, 11:43:24 am »
+4

The worst that can be said is that the phrase "going infinite" is vague or ambiguous.

I would agree that is one of the worst things one could say around here.
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#### werothegreat

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##### Re: Maximum Possible VP?
« Reply #28 on: November 21, 2017, 01:42:23 pm »
0

[...] gain an arbitrary amount of VP.
π is pretty arbitrary, as are -1, i, φ, e, sqrt(2) and Chaitin's constant

An arbitrary positive real integer, happy?  Also, π as a number is not at all arbitrary.
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##### Re: Maximum Possible VP?
« Reply #29 on: November 21, 2017, 04:55:25 pm »
+3

An arbitrary positive real integer, happy?
Oh, I was happy all along, I was just f.ds'ing

You can use the combo to gain 0 VP, which only makes sense if you're making the pedantic point that 0 is non-positive. I think "real" is superfluous, though if people around you think "integers" sometimes refers to the Gaussian ones (ℤ[ i ]), then cool—I want to hang around in your social circle

Also, "positive" implies an ordering; I don't know that there's a default ordering on complex integers (or on the complex numbers), which would push the interpretation of "An arbitrary positive integer, happy?" towards ℤ over ℤ[ i ].

Also, π as a number is not at all arbitrary.
I'll restate the definitions of "arbitrary" I just looked up as "unconstrained", "without system" and "whimsical". Certainly π is not without system; IINM there's a formula mapping n to the nth digit of π. Is this what you mean? If not, what then? My choice of π is somewhat whimsical, though.
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#### ConMan

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##### Re: Maximum Possible VP?
« Reply #30 on: November 21, 2017, 05:01:42 pm »
0

In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
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#### navical

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##### Re: Maximum Possible VP?
« Reply #31 on: November 21, 2017, 05:43:40 pm »
+1

In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.
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#### Donald X.

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##### Re: Maximum Possible VP?
« Reply #32 on: November 21, 2017, 05:45:20 pm »
+10

In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.
I used to think it was dangerous too, but over the course of my life I haven't so much as stubbed my toe over it. I'm beginning to think we can let it back on airplanes.
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##### Re: Maximum Possible VP?
« Reply #33 on: November 21, 2017, 06:03:20 pm »
+4

Dominion is a cool guy. Eh uses 'infinite' and 'unbounded' interchangeably and doesn't afraid of stubbing toe or anything.
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#### fisherman

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##### Re: Maximum Possible VP?
« Reply #34 on: November 22, 2017, 07:10:35 am »
+1

[...] gain an arbitrary amount of VP.
π is pretty arbitrary, as are -1, i, φ, e, sqrt(2) and Chaitin's constant

An arbitrary positive real integer, happy?  Also, π as a number is not at all arbitrary.

Better to say "rational" rather than "real" to make clear you aren't in a number field: https://en.wikipedia.org/wiki/Ring_of_integers.
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#### mith

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##### Re: Maximum Possible VP?
« Reply #35 on: November 28, 2017, 04:54:16 pm »
+6

\$0* Event
Go Infinite

+

*You may only buy this if you are trapped in an infinite unbounded loop of semantics.
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#### pacovf

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##### Re: Maximum Possible VP?
« Reply #36 on: November 28, 2017, 05:05:22 pm »
0

In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?
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##### Re: Maximum Possible VP?
« Reply #37 on: November 28, 2017, 06:13:41 pm »
0

... +aleph1 VP
Are (infinite) ordinal or cardinal numbers most appropriate here?
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#### crj

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##### Re: Maximum Possible VP?
« Reply #38 on: November 28, 2017, 07:38:17 pm »
+3
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#### Cave-o-sapien

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##### Re: Maximum Possible VP?
« Reply #39 on: November 28, 2017, 08:11:35 pm »
+2

I'm no mathematician, but shouldn't it be aleph-null?
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#### navical

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##### Re: Maximum Possible VP?
« Reply #40 on: November 29, 2017, 04:50:33 am »
+2

In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?

Unbounded VP Action \$notenough
+1 VP
You may play this again.

Infinite VP Action \$notenough
+1VP per whole number greater than 0.

The first one can get you any number of VP, but at some point you have to stop, at which point you only have some finite number of VP.
The second one actually gets you infinite VP, because you get them all at once.
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#### LaLight

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##### Re: Maximum Possible VP?
« Reply #41 on: November 29, 2017, 05:01:25 am »
0

In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?

Unbounded VP Action \$notenough
+1 VP
You may play this again.

Infinite VP Action \$notenough
+1VP per whole number greater than 0.

The first one can get you any number of VP, but at some point you have to stop, at which point you only have some finite number of VP.
The second one actually gets you infinite VP, because you get them all at once.

Unbounded VP Action \$notenough
+1 VP
Play this again.
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#### faust

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##### Re: Maximum Possible VP?
« Reply #42 on: November 29, 2017, 06:08:37 am »
0

In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?

Unbounded VP Action \$notenough
+1 VP
You may play this again.

Infinite VP Action \$notenough
+1VP per whole number greater than 0.

The first one can get you any number of VP, but at some point you have to stop, at which point you only have some finite number of VP.
The second one actually gets you infinite VP, because you get them all at once.

Unbounded VP Action \$notenough
+1 VP
Play this again.
It gives you some finite number of VP, until some time in the future when you stop playing the card because you have starved to death.
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#### Chris is me

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##### Re: Maximum Possible VP?
« Reply #43 on: November 29, 2017, 07:09:24 am »
+2

And all of our lives were enriched from this discussion, on a thing that totally matters in this context at all, whether or not the colloquial use of the word “infinite” in a context that literally everyone understands is technically correct or not. F.DS at its absolute finest.
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#### mith

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##### Re: Maximum Possible VP?
« Reply #44 on: November 29, 2017, 09:12:31 am »
+3

I'm no mathematician, but shouldn't it be aleph-null?

Are we now going to quibble over what the transfinite point value of a made-up card should be? Aleph-null is a boring and inadequate number of points to gain given the extreme unlikelihood of ever being able to trigger the buy condit... oh, right.

(With such a transcendental and complex discussion taking place, I'm just trying to keep it real.)
« Last Edit: November 29, 2017, 09:16:55 am by mith »
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• Explorer
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##### Re: Maximum Possible VP?
« Reply #45 on: November 29, 2017, 12:00:06 pm »
+4

Uh... that wasnt aleph-one...
My post assumed the continuum hypothesis
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• Minion
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##### Re: Maximum Possible VP?
« Reply #46 on: November 29, 2017, 12:06:03 pm »
+2

I don't know that there's a default ordering on complex integers (or on the complex numbers), which would push the interpretation of "An arbitrary positive integer, happy?" towards ℤ over ℤ[ i ].
There is no ordering on the complex numbers.
By ordering I here mean "ring ordering", ie one which respects both addition and multiplication.
(ie. x+a<y+a whenever x<y  and 0<a.b  whenever a,b>0.)

I believe the same is true of Z[ i ].
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#### ThetaSigma12

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« Reply #47 on: November 29, 2017, 12:15:29 pm »
+1

Hey I can do math too: 1 + 1 = 2.
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##### Re: Maximum Possible VP?
« Reply #48 on: November 29, 2017, 12:15:59 pm »
+2

There is no [ring] ordering on the complex numbers [nor complex integers].
Absolutely agree. You could do the lexicographic ordering, but no one does that on complex numbers. Failure to respect multiplication is probably the reason why
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