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Jan
26
comment Why does an argument similiar to 0.999…=1 show 999…=-1?
Note that if you use the summation notation to define $x$ as in your edit and then perform the subtraction $0.1x - x$ term-wise, you end up with $\sum^{\infty}_{k=0}{8.1 \cdot 10^k}$, which no longer appears to converge to $0.9$.
Jan
26
comment Why does an argument similiar to 0.999…=1 show 999…=-1?
@Asaf Even restricting the view to math using modern notation, different formal theories can use "$=$" (e.g. see formal theories for lambda-calculus or combinators, which us "$=$" to mean "$=_{\beta}$" or "$=_{w}$", respectively). As for "bad faith," yes, it's certainly bad faith to "assume that someone...has no idea bout" what they're talking about unless you have evidence that this is the case (not posting anything on Math.SE isn't "evidence", it's a lack thereof).
Jan
26
comment Why does an argument similiar to 0.999…=1 show 999…=-1?
@AsafKaragila What...? I don't expect the set of statements acceptable as comments here on Math.SE to be exactly identical to the set of statements acceptable as "things I expect first-year analysis students to expect right off the bat," and I don't see how that's relevant. And it's simply not true that "$=$" only ever has one meaning, especially if you look at old math writing (e.g. Euler's work on convergent series).
Jan
26
comment Why does an argument similiar to 0.999…=1 show 999…=-1?
@Asaf "$=$" doesn't have the same meaning in every context, though. You're right that Geinmachi didn't specify the context for the comment, but there's exactly one context where the statement makes sense, and it's familiar enough (espcially given MichaelSeifert's link for those who aren't familiar with that form of summation) that it's obvious what Geinmachi meant. Arguing otherwise seems to be assuming bad faith.
Jan
11
revised Fixed point combinator (Y) and fixed point equation
Clarify that the cited solution from Hindley is using 'Y' to mean a fixed-point combinator
Jan
11
suggested approved edit on Fixed point combinator (Y) and fixed point equation
Jan
11
awarded  Altruist
Jan
11
comment Wikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no sense
So I am trying to do my research, though I haven't yet had a chance to read the sources sited in this answer. What is "arrogant" about any of this?
Jan
11
comment Wikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no sense
@RobArthan......? That comment is because all quoted content should be properly sourced, and since three sources were listed, there was ambiguity. And I don't understand the impetus for your comment that I should "do some work on this" myself. I'm trying to understand lambda calculus and combinators by reading the Hindley/Seldin text, but that text doesn't seem to be helping me understand how implications can be represented; in fact, they state that lambda calculus cannot be extended to become a first-order (logical) theory.
Jan
8
comment Wikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no sense
Huh. This certainly looks like an answer, or at least most of one! :D You should probably clarify which of your several sources was the source of each particular quote, though. Does Curry ever actually give any rationale for thinking that the standard combinators $\mathbf{S},\mathbf{K}$ preserve the properties of $\mathbf{P}$ when applied to assertions in the new grammar built with $\{\mathbf{S},\mathbf{K},\mathbf{P}\}$?
Jan
8
revised Should you ever stop rolling, THE SEQUEL
added 223 characters in body
Jan
8
comment Should you ever stop rolling, THE SEQUEL
Hahahahaha. I don't think I'm ever going to get back to fixing the arithmetic error, especially since I no longer remember what it is.
Jan
7
comment Wikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no sense
@CarlMummert Thanks for the reference. FWIW, I am reading Hindley and Seldin's text Lambda-Calculus and Combinators, which is a math rather than a CS text. It mentions that "in logical systems based on $\lambda$ or CL, if the system's designer is not extremely careful the corollary may cause paradoxes", but so far (I've read the first four chapters) it has made no mention of how implication can be integrated into lambda-calculus.
Jan
6
comment Wikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no sense
The "principle of explosion" comment may refer to the fact that if $(rr)$ is false, then $(rr)→y$ (assuming the standard first-order logic meaning for $→$) is trivially true. But in that case it's not clear why "$(rr)→y$ is true" is a contradiction.
Jan
6
revised Wikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no sense
deleted 2 characters in body
Jan
6
asked Wikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no sense
Jan
6
comment Fixed point combinator (Y) and fixed point equation
Okay, the other part of my confusion (which was mostly clarified by reading further in the book) is that the first equation, $xy_1y_2\dots y_n = Z$, is any arbitrary equation (i.e. not a formula already known to be satisfied by $=_{\beta, w}$) where one side starts with $x$. This makes the "solve for $x$" definition make a lot more sense.
Jan
5
comment V.I. Arnold says Russian students can't solve this problem, but American students can — why?
@HenningMakholm I (and presumably the other two) am not familiar with the phrase "drop (an altitude) onto". I interpreted it simply to mean that the height in (at least) one direction was 6. If I had been in an exam situation or some other context where I needed to answer the question definitively, I'd have recognized my uncertainty and sought clarification.
Jan
4
comment V.I. Arnold says Russian students can't solve this problem, but American students can — why?
@IanF1 I interpreted "it" to refer to the entire triangle, i.e., "one of the altitudes of the triangle is 6." I realize that the original phrasing is probably supposed to indicate that the altitude perpendicular to the hypotenuse is 6, but like several other people commenting, I don't remember ever hearing the "dropped onto" terminology before, so my guess was the one that made it possible for the triangle to exist. If I were a student and this were an exam, I'd simply have asked for clarification.
Jan
4
comment V.I. Arnold says Russian students can't solve this problem, but American students can — why?
@HenningMakholm slebetman, ETHproductions, and I presumably all assumed that "it" referred to the triangle itself.