You can't be serious with C++. I've tried (see my bio if you have any doubt;-) You should rather consider one of the many C-- in existence. Some tidbits:
C-- is a subset of all ambiguous constructs which could be removed from any C++
extension without impact on general code quality. This naturally include all
standard C and C++ constructs.
All new features range from "useless" to "potentially disastrous". The C--
reserved words that fall in the last category do not contain an asterisk (*).
The current implementation (V21.13) is a post-processor written in FORTRAN.
It handles errors generated by the C compiler and interpolates with the C--
source code to create an MS-DOS batch file, which more or less does the same
thing as what your C-- program intended to do, only slower.
This implementations makes it easy to port the C-- compiler, provided there
is a FORTRAN compiler, a C compiler and an MS-DOS batch file interpreter.
IBM PC/DOS version is currently in beta test.
OK, I wrote all that crap a long time ago, and it shows a bit... But I may have been one of the first ones to propose comments ending in \\ (for left-handed people), a C++ compatible implementation of comefrom, function inheritance, #try.. #catch (to try and compile something), and a few others niceties. Too bad I did not finish it, I still had a lot of work to do on short long, dereferencing of float, dodecadecimal numbers, probabilistic switch, etc.
The extended type information would be quite welcome... if it extends to the C++ code itself and allows full reflection to be implemented in C++. And I doubt they will ever go that far.
By the way, if you believe that we can improve over C++, come and help me implement LX... In my very biased opinion, this language is insanely better than C++. It is also one of the least successful Open Source projects in existence:-)
I personally don't feel the need to copy any of my old floppies. All that I ever had on floppies and that mattered to me is now somewhere on my current hard disk (and a few past ones). All of it takes only a fraction of my 18GB drive. Assume I had 100 floppies that mattered: that's less than 200MB, which you can copy in a few seconds on modern digital media.
As a matter of fact, each time I get a new computer, I copy all the stuff from the old one, and it takes only a fraction of the space. The 40MB of my first (Atari ST) hard disk are there. The 160MB of my first Mac hard disk (120MB left after I copied the Atari hard disk onto it) are there. And so on.
The real issue is binary formats that have been forgotten. For instance, I have source code of programs I wrote in GFA Basic (a Basic for the Atari ST, in case you wonder.) But emulators come to the rescue there. Today, I can run Atari programs faster than on the real machine.
1/ Words such as "absurd" and "existance" or "doesn't work" do not have much place in my own understanding of mathematics.
2/ The proof you gave, at best, proves that the 'x' solution of the above is not a natural number. The exact same reasoning you gave proves that there is no solution to x+1 = 0. Do you deny the "existence" (whatever meaning you give to that) of the number -1?
3/ You use a recursive proof which you claim as being invalid in some other posts. This is internal inconsistency. While this has no mathematical value whatsoever, this puts in my "brain" a serious doubt regarding the rest of your "reasoning."
So you say that infinity has no place in your own mathematics. Fine. Then, you are using the word "mathematics" in a sense which is not the sense I use myself.
To me, mathematics is a methodology for reasoning derived originally from idealized physical entities (such as square, lines, etc), but which has since then been formalized using logic, axioms and formal derivation. This formalism is useful because it has been shown by historical experience that it helps us "discover" and "model" physical properties.
Complex numbers are a very good example. The original "existence" of complex numbers is the observation that you can build a set of consistent rules with numbers built using the "imaginary" solution of x * x + 1 = 0. Even better, the resulting rules are quite close to those that we have previously defined for "natural" numbers.
But the most interesting thing about complex numbers is that they turn out to be a very good way to describe, for instance, electromagnetic fields or wave equations. And the circle is complete, we are back to "real" things. The same thing happens to infinity. A physicist will use an infinite line as the model because it works well, regardless of the existence of any such line in "the real world." Remind me of the old joke about the physicist asked to model a horse race, and who starts with "let's assume a spherical horse." That's really all there is.
So mathematics, in my opinion, do not work because of their abstract beauty or whatever. They work because they allow us to make predictions for what we call the "real" world.
As a last comment, the use you make of "absurd" or "beauty" makes *you* behave as a religious zealot who owns The Only Real Trush of The Saint Intuitionism. And, frankly, I don't see why the fact that Cantor was Jewish has anything to do with the quality of his maths. Oh, or maybe it is because 42 is the answer?
Proposed definition of infinity:
I call "infinite" the solution of: x * 0 = 1.
This definition takes my brain about 1/2 second to process.
Historically, much of the mathematics have been built by defining something as the result of an equation with no result. For instance, x*x=-1 yields the complex numbers, x*x=2 yields the non-rational numbers, etc.
There are other non textual programming abstractions out there. The Mozart project is one, but there are others such as Microsoft's own Intentional Programming. You can find other related links from the Mozart page.
Also: contrary to what several posters said, the government is not responsible for the lawsuit. The initial lawsuit was filed by several french associations, including an anti-racism association and a Jews victims associations, IIRC.
It's funny, because I have designed such a non-C based language. And it is called... "LX", like the login name of the original poster. No, that wasn't me.
The language is shortly described there. It is designed to integrate in a visual, language-agnostic programming environment called Mozart. It is open-source, you can download and try it.
Of course, at this point, it won't do much for you. As a proof that it can do more than LX, Mozart contains a Java to Java translator that can serve as a pretty-printer and be used to implement all sorts of Java extensions. LX parses and does some basic semantics analysis, but nothing very serious yet.
Getting rid of the C legacy enables tons of things. Such as optimizing on modern processors:-)
Slashdot Mirror
You can't be serious with C++. I've tried (see my bio if you have any doubt ;-) You should rather consider one of the many C-- in existence. Some tidbits:
C-- is a subset of all ambiguous constructs which could be removed from any C++ extension without impact on general code quality. This naturally include all standard C and C++ constructs.
All new features range from "useless" to "potentially disastrous". The C-- reserved words that fall in the last category do not contain an asterisk (*).
The current implementation (V21.13) is a post-processor written in FORTRAN. It handles errors generated by the C compiler and interpolates with the C-- source code to create an MS-DOS batch file, which more or less does the same thing as what your C-- program intended to do, only slower. This implementations makes it easy to port the C-- compiler, provided there is a FORTRAN compiler, a C compiler and an MS-DOS batch file interpreter. IBM PC/DOS version is currently in beta test.
OK, I wrote all that crap a long time ago, and it shows a bit... But I may have been one of the first ones to propose comments ending in \\ (for left-handed people), a C++ compatible implementation of comefrom, function inheritance, #try .. #catch (to try and compile something), and a few others niceties. Too bad I did not finish it, I still had a lot of work to do on short long, dereferencing of float, dodecadecimal numbers, probabilistic switch, etc.
See Mozart to see what I mean.
By the way, if you believe that we can improve over C++, come and help me implement LX... In my very biased opinion, this language is insanely better than C++. It is also one of the least successful Open Source projects in existence :-)
I personally don't feel the need to copy any of my old floppies. All that I ever had on floppies and that mattered to me is now somewhere on my current hard disk (and a few past ones). All of it takes only a fraction of my 18GB drive. Assume I had 100 floppies that mattered: that's less than 200MB, which you can copy in a few seconds on modern digital media.
As a matter of fact, each time I get a new computer, I copy all the stuff from the old one, and it takes only a fraction of the space. The 40MB of my first (Atari ST) hard disk are there. The 160MB of my first Mac hard disk (120MB left after I copied the Atari hard disk onto it) are there. And so on.
The real issue is binary formats that have been forgotten. For instance, I have source code of programs I wrote in GFA Basic (a Basic for the Atari ST, in case you wonder.) But emulators come to the rescue there. Today, I can run Atari programs faster than on the real machine.
1/ Words such as "absurd" and "existance" or "doesn't work" do not have much place in my own understanding of mathematics.
2/ The proof you gave, at best, proves that the 'x' solution of the above is not a natural number. The exact same reasoning you gave proves that there is no solution to x+1 = 0. Do you deny the "existence" (whatever meaning you give to that) of the number -1?
3/ You use a recursive proof which you claim as being invalid in some other posts. This is internal inconsistency. While this has no mathematical value whatsoever, this puts in my "brain" a serious doubt regarding the rest of your "reasoning."
So you say that infinity has no place in your own mathematics. Fine. Then, you are using the word "mathematics" in a sense which is not the sense I use myself.
To me, mathematics is a methodology for reasoning derived originally from idealized physical entities (such as square, lines, etc), but which has since then been formalized using logic, axioms and formal derivation. This formalism is useful because it has been shown by historical experience that it helps us "discover" and "model" physical properties.
Complex numbers are a very good example. The original "existence" of complex numbers is the observation that you can build a set of consistent rules with numbers built using the "imaginary" solution of x * x + 1 = 0. Even better, the resulting rules are quite close to those that we have previously defined for "natural" numbers.
But the most interesting thing about complex numbers is that they turn out to be a very good way to describe, for instance, electromagnetic fields or wave equations. And the circle is complete, we are back to "real" things. The same thing happens to infinity. A physicist will use an infinite line as the model because it works well, regardless of the existence of any such line in "the real world." Remind me of the old joke about the physicist asked to model a horse race, and who starts with "let's assume a spherical horse." That's really all there is.
So mathematics, in my opinion, do not work because of their abstract beauty or whatever. They work because they allow us to make predictions for what we call the "real" world.
As a last comment, the use you make of "absurd" or "beauty" makes *you* behave as a religious zealot who owns The Only Real Trush of The Saint Intuitionism. And, frankly, I don't see why the fact that Cantor was Jewish has anything to do with the quality of his maths. Oh, or maybe it is because 42 is the answer?
Proposed definition of infinity:
I call "infinite" the solution of: x * 0 = 1.
This definition takes my brain about 1/2 second to process.
Historically, much of the mathematics have been built by defining something as the result of an equation with no result. For instance, x*x=-1 yields the complex numbers, x*x=2 yields the non-rational numbers, etc.
There are other non textual programming abstractions out there. The Mozart project is one, but there are others such as Microsoft's own Intentional Programming. You can find other related links from the Mozart page.
Also: contrary to what several posters said, the government is not responsible for the lawsuit. The initial lawsuit was filed by several french associations, including an anti-racism association and a Jews victims associations, IIRC.
Of course, at this point, it won't do much for you. As a proof that it can do more than LX, Mozart contains a Java to Java translator that can serve as a pretty-printer and be used to implement all sorts of Java extensions. LX parses and does some basic semantics analysis, but nothing very serious yet.
Getting rid of the C legacy enables tons of things. Such as optimizing on modern processors :-)