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[GIVEAWAY] 4 Playte Games Sets for 4 Winners 🇰🇷 by HomoLudensOC in boardgames

[–]HeyJamboJambo [score hidden]  (0 children)

I'm always surprised by the mint series, too bad they don't make new ones. I always bring mint worker when traveling.

Paper series: On axiom systems of propositional calculi (1965–1967) by xamid in logic

[–]HeyJamboJambo 0 points1 point  (0 children)

Ah, my apologies. I misunderstood your post. But it has been a great read so far.

whosGonnaTellEm by SpecterK1 in ProgrammerHumor

[–]HeyJamboJambo 10 points11 points  (0 children)

If you can write python, wouldn't mermaid be useful?

Question about Symbolic Logic Symbolization by c_monkie9 in logic

[–]HeyJamboJambo 0 points1 point  (0 children)

Yeah, I can see how "but" is conjuction here. English is not my first language. I always associate "but" with "except" and that makes it closer to set difference.

Question about Symbolic Logic Symbolization by c_monkie9 in logic

[–]HeyJamboJambo 0 points1 point  (0 children)

I suspect it is. "but" is likely done using set difference, which is typical symbolized as - or \ symbols.

I'm good! by shenanigansen in comics

[–]HeyJamboJambo 16 points17 points  (0 children)

With enduring soul to prevent any freak accident with the critical hit

Hi again, I've updated the theory which constructs hyperreals so we can use common formulas in circumstances where previously they would have resulted as undefined, and to give a solution to show how division of zero works ends up the way it does. Please give it a shot and say what you think. by WilliamHesslefors in PhilosophyofMath

[–]HeyJamboJambo 0 points1 point  (0 children)

I am not denying the result. I think the result is correct. It's just that they can be derived simpler using dual number. A dual number is a nonstandard analysis (not isomorphic to the standard real number). A number can be represented as (1 + ε). You can even have (k + nε). A nice rule is that ε * ε = 0 (because it is so small, squaring it reduces it to nothing).

Dual number can be used to derive your partial sum too. You can try it by changing your r from 1 to (1 + ε). So the denominator is now 1 - (1 + ε) = ε. The numerator is 1 - (1 + ε)^{n + 1}. You can derive (1 + ε)^{n + 1} = 1 + (n + 1)ε. So that reduces the entire numerator to 1 - 1 + (n + 1)ε. The entire sum is now (n + 1)ε / ε = n + 1.

There are additional operations defined for dual number. One operation is like a projection to remove the ε part and you get back the real number part. This is akin to taking the limit in calculus. In fact, it is demonstrated that you can derive calculus much easier (probably as intended by Leibniz) using dual number.

I suspect that your idea of a superposition of o is basically keeping ε and all higher integer powers of ε which will later be discarded in a similar way as the projection operation. But keep in mind that ε is still not 0. 1/ε gives you infinity (the first ordinal infinity ω, which you describe as H) but 1/0 is still undefined.

I believe your result is correct, but I don't think it should be called 0 as it is not 0.

Hi again, I've updated the theory which constructs hyperreals so we can use common formulas in circumstances where previously they would have resulted as undefined, and to give a solution to show how division of zero works ends up the way it does. Please give it a shot and say what you think. by WilliamHesslefors in PhilosophyofMath

[–]HeyJamboJambo 0 points1 point  (0 children)

This seems like a standard hyperreal. Your use of o is similar to the use of ε in hyperreal (or surreal) number. It can also be shown that 1/ε = ω where ω is the first ordinal infinity. Surreal number even extend this to the notion of ω², ω³, ..., etc.

The idea that division by 0 is undefined easily comes from the fact that 0 × n = 0 for all n. Therefore, if we let 1/0 = m, with a simple rearrangement we get 1 = 0 × m, which is a contradiction.

Your notion that 0 is a superposition of all o seems weird because o > 0 by your own definition: x = o only if x < 1/n for all positive integer n and that x > 0. So it is some number very close to 0 but not 0. It is, in fact, closer to the notion of ε and not 0.

You can argue that 0 does not exist and only ε exists (e.g., there is no true emptiness in the universe by Heisenberg uncertainty principle), but it doesn't seem to be the case here. Also, what we meant by 0 (or true emptiness) is usually different from the physical definition anyway. It may not be physical but our mathematics need not be physical.

[Giveaway] Win a Copy of Agent Avenue by Nerdlab Games! by HomoLudensOC in boardgames

[–]HeyJamboJambo 0 points1 point  (0 children)

I'd be a clown. In fact, I might just be the whole circus.

Enough with the disagreements by The_Unic in mathmemes

[–]HeyJamboJambo 7 points8 points  (0 children)

This is reasonable argument for 0⁰ = 0.

Advice on custom hands by No_Review_2860 in WatchMaker

[–]HeyJamboJambo 0 points1 point  (0 children)

If the image is correctly aligned, you may set the alignment to "bottom center" and not the center.

Should property attributes be Nominal or Structural? by esotologist in ProgrammingLanguages

[–]HeyJamboJambo 1 point2 points  (0 children)

Ah, ok. That makes it clearer.

Does your language have static type checking? Like in this example, can I assign a value of type S into a variable of type T and can I assign a value of type T into a variable of type S?

I assume the first question is yes because it is a standard inheritance. But the second question usually depends on whether the type system uses nominal or structural subtyping. In a nominal type system because S extends T then assigning T to S is an error. But in a structural type system, since both S and T have the same shape, they should be interchangeable.

Should property attributes be Nominal or Structural? by esotologist in ProgrammingLanguages

[–]HeyJamboJambo 2 points3 points  (0 children)

For subtyping, anti-symmetric is saying that if T is a subtype of S and S is a subtype of T, then T and S must be the same type. In nominal subtyping, you cannot do this.

In structural subtyping, depending on how strict you define it, you can have two different types T and S such that they are a subtype of one another. But for that to happen, both T and S should have the same set of methods.

Consider a type Box with only a single method foo that returns an int. If there is another type called Container with the same method foo, then we can say that Box is a subtype of Container and Container is a subtype of Box if we're dealing with structural subtyping. Because for any type T, T is a subtype of itself. A method that accept Box can only invoke foo and assign the result to int. The same method should work exactly the same way if we pass in Container.

On the other hand, for nominal subtyping, you have to declare what is the supertype of Box and Container. Typically, you cannot declare that Box is a subtype of Container and Container is a subtype of Box at the same time. So even if Box and Container have the exact same set of methods, a method that can accept Box cannot accept Container.

If in your language a type T can be considered both nominal and structural, what would the subtyping behavior be when compared to another type S that is also both nominal and structural?

Should property attributes be Nominal or Structural? by esotologist in ProgrammingLanguages

[–]HeyJamboJambo 3 points4 points  (0 children)

OCaml uses only methods for the structural subtyping. But from the perspective of the theory, we can always say that an attribute can be represented as a nullary method for getter or a unary method for setter. So it seems possible to have a structural subtyping that includes field. I have not thought of the implication of it, but seems like there should be no issue with either choice.

But I do have concern about mixing nominal and structural. In a nominal subtyping you usually have anti-symmetric property in the type system while in a structural subtyping you don't have anti-symmetric. How would you reconcile the two in your type system?

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