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Mathematics is shit

Name: Anonymous 2012-01-09 1:19

Just look at these ugly swatches of code:
http://www.cse.unt.edu/~idl99/Proceedings/ahn/img50.gif
http://www.cse.unt.edu/~idl99/Proceedings/ahn/node8.html

That is what you get, when programming immitates math. Even Java and PHP looks beautiful compared to that. Mathematics should be banned as a harmful and obfuscated teaching.

Name: Anonymous 2012-01-09 4:27

>>35

In testing one must find a way to repeat the erroneous behavior so that the cause can be identified. I am an expert [i][o][u][b]BBCODE QUALITY ASSURANCE ENGINEER[i][o][u][b]

Name: Anonymous 2012-01-09 4:49

>>40
(loop for x from 0
      for y = nil then (union (list x) y) do
     (format t "~a = ~a~%" x y))

Name: Anonymous 2012-01-09 4:57

>>42
Minor error. Self fix.
(loop for x from 0
      for y = nil then (union (list (1- x)) y) do
     (format t "~a = ~a~%" x y))

Name: Anonymous 2012-01-09 5:10

>>12
That's the ultimate problem: A symbol is MEANINGLESS without MEANING.
I think that's what >>1 (or yours?) problem is: you're forgetting that a string of symbols can be interpreted and has a meaning, or to say it more clearly: semantics. Math talks about relations and behavior of very abstract objects, that is, of truth about general objects and structures - if you added real-world characteristics to them, the truth would remain unchanged, the only thing that sets them apart are very simple general properties and the rest is irrelevant. To put it another way, finite numbers will always have the same properties given the standard interpretation of arithmetic, regardless of whatever other properties you ascribe to those numbers (such as beings rocks, bits, atoms, whatever) - math can be seen to describe these general timeless relations, the syntax is less important as long as it can be learned and someone can interpret it, if you wanted to, you could do all your inferences and syntax in lisp, despite that most mathematicians tend to use more 'natural' styles that they're now used to (I'm not claiming that the syntax they use is that good, just that it works).

>>40
I know that you're probably an ultrafinitist, but theorem provers/formal systems can easily talk about things they can't reach. Infinity for me is just a way of talking about uncomputable properties, which computable objects(such as programs) can have, for example, wether a program halts or not, or more general convergence-related properties. Infinity is not a meaningless concept, even if you never directly touch it, but it's always needed when you want to go meta(such as about 'all' programs or 'all' functions). Since you seem very pragmatic and don't like to talk about such general things, maybe math isn't for you (not talking about syntax here, but about semantics), however these 'unreachable' concepts are important and they lead to deeper truths which will nevertheless hold, regardless of what you think about 'infinity' or wether you want to contemplate it at all.

Name: Anonymous 2012-01-09 7:33

>>44
it's always needed when you want to go meta(such as about 'all' programs or 'all' functions).
There is no such thing as "all". It's a buzzword.

Name: Anonymous 2012-01-09 7:47

>>45
And this is why you'll never understand why anything at all works.

Name: Anonymous 2012-01-09 8:22

Please, everyone in this thread, don't feed the trolls.

Name: Anonymous 2012-01-09 8:26

>>46
please, define "understand"

Name: Anonymous 2012-01-09 8:51

>>45
Here's a meta-property which will apply for any(all) programs: it will either halt or not halt (given an ideal machine).

Name: Anonymous 2012-01-09 8:52

>>49
I can't decide.

Name: Anonymous 2012-01-09 8:56

>>49
There is no such thing as "all programs". There are only written programs stored on some media, like your /dev/hdd.

Name: Anonymous 2012-01-09 9:42

>>51
So you don't accept any abstract concepts, fine then, then you don't need to talk about math or computer science, as they don't study the behavior of actual programs, but the behavior of ideal programs. If your actual programs match the behavior of ideal programs, that's only because the physical implementation is close enough. However, how if you insist on not giving any privileges to the abstract and only giving privileges to physically existing things, what do you think this universe is? You can't even make the hypothesis that it exists as a coherent structure, or if you do, you can only infer it indirectly through your observations, thus you're making use of the abstract. If you don't make any such hypothesis, the only thing that you know are your perceptions at the moment (here and now) and your possibly unreliable memories. Sounds like a bad way to waste one's intelligence.

Name: VIPPER 2012-01-09 10:02

What does /prog/ think of the lambda calculus? No doubt you guys looked into it.

Name: Anonymous 2012-01-09 10:19

>>53
It has ugly syntax. (/\crap.crap /\crap.crap) /\crap.crap looks like crap.

Name: Anonymous 2012-01-09 11:01

Mathematics is purely functional, symbolically evaluated, has unbounded recursion, and allows new ad hoc operators, functions, constants, variables, and orders of evaluation to be defined. APL is a formal language defined in terms of mathematics, described in terms of mathematical operations as a notation used in the formal description of the System/360, making APL functions "overloaded operators" of mathematical notation.

Name: Anonymous 2012-01-09 13:59

>>44
The symbol _never_ has meaning, the way it is used and related to by other symbols defines its meaning.

Mathematics /is/ about real-world structures, that is what mathematicians do, they define a universe and put the objects into it and declare themselves to have seen some godlike properties despite declaring in advance what'll happen.

There is a simple reason why lambda calculas took so mind-boggling long to develop, and why lisp is still confusing to 90% of programmers:

They can't CONCEIVE of a thought that has no label, no name, no representation other than it's relations. In NO mathematical axiomatic methods, proofs, anything, do you have things like 1. An unbounded space 2. there is NOT, AND, NOR, and they can feed into eachother. 3. There is time.

ALL proofs start with defining names, and only afterwards do they care of relations. It is of no use to anyone if someone can memorize every language in the world if they don't know what any of the words mean, and this is what the discussion has been in the thread, so good job taking one quote of someone out of context and being retarded to the rest of the thread.

Back in my day trolling meant something.

Name: Anonymous 2012-01-09 14:18

Mathematics /is/ about real-world structures, that is what mathematicians do, they define a universe and put the objects into it and declare themselves to have seen some godlike properties despite declaring in advance what'll happen.
They are idealized structures which soon end up being far divorced from what is physically computable (but not divorced from what is effectively computable, or Turing computable).
They can't CONCEIVE of a thought that has no label, no name, no representation other than it's relations.
Use gensyms, graphs or whatever you wish.
In NO mathematical axiomatic methods, proofs, anything, do you have things like 1. An unbounded space 2. there is NOT, AND, NOR, and they can feed into eachother. 3. There is time.
1. Most proofs that I've seen have unbounded spaces or domains. Most proofs in arithmetic are done over natural numbers, which are unbounded.
2. You can define in relations in terms of each other. As far as logic is concerned, you don't really need all 3 of those. A NAND or NOR is sufficient.
3. Time is useful as far as describing computations, but it can always be abstracted away as a relationship between states. f:N->N, f computable, f(time)=state. Possible recursive definition: f(0)=initial_state. g:N->N, g computable, f(n)=g(f(n-1)), where g just describes how to compute the next state given the current state. Want to know what g's implementation would be like? Take a look at a Turing machine or Primitive Recursion Functions/Primitive Recursive Arithmetic.
good job taking one quote of someone out of context and being retarded to the rest of the thread.
I only answered it once, well, twice now, counting your answer, probably again out-of-context.

Name: Anonymous 2012-01-09 14:32

>>57
You're still a moron with no possible future as a computer programmer.

Name: Anonymous 2012-01-09 14:38

>>58
Back to /bankruptcy court, kodak_gallery_programmer/

Name: Anonymous 2012-01-09 14:42

>>59
Most proofs in arithmetic are done over natural numbers, which are unbounded.

Hey dipshit, if natural numbers were unbounded, then they couldn't be countable. I believe the correct term that you're looking for is "countably infinite". But I could be wrong since I'm only a programmer and you're only a toilet scrubber.

Name: Anonymous 2012-01-09 14:45

>>56
There is a simple reason why lambda calculas took so mind-boggling long to develop,
... What?

Name: Anonymous 2012-01-09 14:49

>>60
Oh, fuck off, kodak.

Unbounded just means not limited by any upper bound. There is no finite maximum number k which is greater than all finit natural numbers. Bounded means that there is some upper bound which is greater than all elements in some domain. Countably finite is a correct way to refer to naturals as their cardinality is aleph null. Another way is calling them enumerable.

Name: Anonymous 2012-01-09 14:50

>>60
There are several definitions of bounded and unbounded and none of them involve countability. Given the absolute value as the metric the natural numbers are uncountable.

Name: Anonymous 2012-01-09 14:51

>>60
Natural numbers are unbounded, they have no upper bound. That's why they're (countably) infinite.

Name: Anonymous 2012-01-09 14:51

>>63
Correction, the last word should be unbounded.

Name: Anonymous 2012-01-09 14:54

>>62
There is no finite maximum number k which is greater than all finit natural numbers.

Yes there is you mental midget. It's called k+1.

Countably finite is a correct way to refer to naturals as their cardinality is aleph null.

Then why didn't your dumbass say that in the first place? Wait never maind. I don't wanna know. I'm afraid that your response is gonna lower my IQ.

other way is calling them enumerable.

No.

Name: Anonymous 2012-01-09 14:55

>>65
Yes, naturals are countable. Reals are not. Cantor's diagonalization proof shows that. If you're a classical finitist, you may not think reals can exist in nature, but I do think considering  computable reals should be fine(computable reals are countably infinite though, have a measure 0 within the whole of real numbers). However that shouldn't matter, even if they turn out to be useful fictions instead of something stronger: they are a good bet which allows speedup, and so far the bet has been giving useful results, even though we don't know if it's really a correct bet (if ZFC or some other infinitary system is consistent).

Name: Anonymous 2012-01-09 14:57

>>66
If k is maximum, then k+1 exists, which contradicts your upper bound assumption. Learn to read.
No.
You're stupid and you know nothing of computability/recursion theory. Just get out of here or read a book already.

Name: kodak_gallery_programmer !!kCq+A64Losi56ze 2012-01-09 14:57

>>64
Natural numbers are unbounded, they have no upper bound. That's why they're (countably) infinite.

It depends you idiot. What happens if I have some function called f defined over a set of natural numbers that doesn't satisfy either the onto on one-to-one condition that is necessary for countability?

Exactly. Now shut your pie hole and get ready to go scrub another toilet.

Name: kodak_gallery_programmer !!kCq+A64Losi56ze 2012-01-09 14:59

>>68
You're stupid and you know nothing of computability/recursion theory. Just get out of here or read a book already.

I never said nor implied recursion theory you idiot. Good lord. Have you ever done a formal math proof in your entire life?

Name: Anonymous 2012-01-09 15:00

The natural numbers are countably infinite but also unbounded given a metric that makes geometrical sense when used on the real numbers. There is no sense in talking about boundedness without a metric, I think you could easily construct a metric in which an open ball of radius 1+epsilon centered on any natural number would extend to every other natural number for every epsilon > 0 and so the set would be bounded with respect to that metric.

Name: Anonymous 2012-01-09 15:04

>>69
It depends you idiot. What happens if I have some function called f defined over a set of natural numbers that doesn't satisfy either the onto on one-to-one condition that is necessary for countability?
Then you have said nothing about the countability of that set, you may always create a function with those properties from any set to another set.

Name: Anonymous 2012-01-09 15:04

>>69
What happens if I have some function called f defined over a set of natural numbers that doesn't satisfy either the onto on one-to-one condition that is necessary for countability?
We were talking about the set of naturals, not on functions defined on them.

As for the other posts: most of the posts were talking about naturals, not reals. An upper bound for a set of naturals just means the set has a finite cardinality.

Name: kodak_gallery_programmer !!kCq+A64Losi56ze 2012-01-09 15:07

>>72
Are you really this stupid? Having a set defined by the natural numbers is a way to define a set.  This is something you learn in the first week of set theory you dumbass.

Name: >>72 2012-01-09 15:08

>>69
By the way any subset of a countable set is countable, it's trivial to construct an isomorphism (f(x) = x) from the subset to the set.

Name: kodak_gallery_programmer !!kCq+A64Losi56ze 2012-01-09 15:12

>>75
By the way any subset of a countable set is countable

That is incorrect you mental midget. What happens if I have a set of real numbers in the interval [0,1]. The interval, which is defined on the set of natural numbers is countable. However, the subset of this interval isn't.

Name: Anonymous 2012-01-09 15:12

>>74
Having a set defined by the natural numbers is a way to define a set.
I never stated otherwise you fucking moron, you made a false statement that a set consisting solely of natural numbers might not be countable, they always are and the proof is trivial but apparently your monkey ass is probably too retarded to pass basic mathematics.

Name: kodak_gallery_programmer !!kCq+A64Losi56ze 2012-01-09 15:13

>>73
I was thinking of some kind of enumerated list that maps to a set of natural numbers.

Name: Anonymous 2012-01-09 15:15

>>76
Listen you piece of shit retard, [0,1] isn't a subset of the natural numbers you fucking moron, do you sincerely believe that 0.5 is a natural number?

Go read any basic book on mathematics you fucking moron, how are you even able to operate a fucking computer is beyond me.

Name: Anonymous 2012-01-09 15:15

>>77
Stop projecting and go scrub another toilet you fucking idiot. Again, you have no possible future as a computer programming.

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