HeeHee. I have run with some of the best in my generation. Your attack is a bit feeble. Most electrical engineers involved in electronic design out of necessity become applied mathematicians. I worked on an IC that did analog computation in the control of an RGB laser video projector. Analog solutions to differential equations. There wasn't enough room on the chip to instantiate a processor core. The group spoke calculus.
As Homs are the last resort of incapable.
If you can not follow my reasoning that is not my problem. Perhaps you do not have the experience and depth.
Sorting and searching? You mean like hashing, bubble sort, and halving algorithms? Knuth's text Seminumerical Algorithms was part of my library. Parsing strings? For fun I wrote n RPN calculator parsing text strings and processing equations..
What have you done lately?
Reminded myself that strings are not numbers.
You should try this sometime. It might help you understand why you're wrong this once, whatever your strengths may otherwise be (accepted you made an oopsie obviously isn't one of them). The fastest sorting algorithm will throw a wrong result fast when your function expects numbers and is fed strings.
And do I really have to remind you who started with the ad hominems? Does "Do me a favor, if you do any computaional work on a building, bridge, or jet let me know so I can avoid them..." sound like something you may have typed?
The ad homs started with a FUCK or two and personal attack on me. Water off a ducks back..
You mean when I wrote "What are you, a javascript programmer?" in
on page 35?
I am far from infallible. I made mistakes over the course of the debate. The usual problem solving process.
The only right course of action at this point is to admit those mistakes and move on, even if they make your entire argument ctrumble.
The mutually exclusive claim that an infinite decimal can equate to a finite number is impossible to reconcile.
Wrong. The decimal is a composite
label in a specific
language - the language of decimal notation. The properties of the labels are not required to map in any trivial way to the properties of the entities they refer to. Saying they are is not unlike claiming that the English sentences "We both know all each other's thoughts" and "I know everything about what you think and you know everything about what I think" cannot be equivalent because one is longer, or because one contains coordination ("and") and a couple of embedded clauses while the other is a single clause sentence.
In linguistics as in mathematics, you need to look at the semantics of the atoms of meanings in a clause and the syntax used to combine them to determine a clause's meaningth. In order demonstrate that two clauses differ in meaning, you need to find a scenario where they're
not interchangeable. The sentences "I saw you leave" and "I saw that you left", while similar in meaning, are not interchangeable because there are situations in which one is TRUE and the other is FALSE: If I see indirect evidence that you left, e. g. the front door is doubly locked and your jacket is not in its usual place, I might say the latter but not the former.* When we apply the same logic to the first pair of sentences, the ones about knowing your thoughts and knowing what you think, we fail to find such a situation: The two sentences reflexively imply each other, the other has to be true too. They form an equivalence class.
The same holds for 0.999...., 1.000 and 1: In any operation using 0.999..., and that does not itself terminate in an expression with a recurring "9" at the end (in which case we still don't know whether they're the same) it can be replaced with 1.0 without changing the result. (0.999... + 0.999...) - 0.999... = 1.0,
just like (0.999... + 0.999...) - 1.0 = 1.0 and
just like (1.0 + 1.0) - 1.0 = 1.0
Incidentally, 1.0 is
also an infinitely recurring decimal: 1.(0). The fact that we allow ourselves to drop recurring 0s but not recurring 9s from the representation is a mere convention -- and one that actually opens the door to ambiguities in the real world: When we don't know whether we're dealing with precise or rounded values, 1.0 is ambiguous between "exactly one" and "an unspecified value to be rounded to 1 at a precision of one digit after the point".
0.(9) carries no such ambiguity - it always is "exactly one".
By skipping the step of equivalence testing and declaring that two different labels
must refer to two different things, you're literally mistaking the map for the countryside.
The geometric series formula itself is derived by taking a limit to infinity, it is not exact.
Yes, it is.
n/10/[1 - 1/10] as n-> 9 the function goes to 1/1. That is what I am saying. The fact that the last possible decimal is 0.999.. means the only solution is 1/1, it does not mean 0.999.. has a finite value any more than 0.333.. does.
Both do have a finite value. I hate repeating myself, but the fact that the value of 0.(3) cannot be expressed in a fully explicit finite string in base 10 is a well-known bug of base 10, not a property of the number. The same number in base 12 is 0.4 exactly. Claiming that the number "doesn't have a finite value" is like saying that Russian uses an awful lot of digits in their words because you used the wrong decoding for the Cyrillic script and get the like of '\u0416' in your output.
.111... 1/9
2/9
3/9
4/9
5/9
6/9
7/9
8/9
9/9
See the pattern? The fact that 0.999... results in unity has no more significance than 0.333... Using the same formula the two results are to be taken differently? 1/3 yields 0.333... not finite, but 1/1 is unity but we take that as meaning 0.999.. = a finite 1? I do not. That is the end of my argument. Refuted my reasoning.
There's no argument. You're confusing the label with what it refers to. In duodecimal notation (base 12), the results of the exact same series of divisions is exactly:
1/9 = 0.14
1/9 = 0.28
3/9 = 1/3 = 0.4
4/9 = 0.54
5/9 = 0.68
6/9 = 2/3 = 0.8
7/9 = 0.94
8/9 = 0.A8
9/9 = 1/1 = 1
Tell me again how the
numbers (not the labels we use in decimal as a workaround for the fact that decimal is ill-suited to deal with fraction of 3n) are infinite?
If this were a situation that I had to resolve I'd head over to the University Of Washington and find an mathematician. I have talked to UW profs in the past on some problems.
Take care not to be blacklisted as "that annoying woo peddler" when you come to them with things you should have learned before you learned to drive.
*) I'm not actually 100% whether this inequality holds for the English sentences. It does for their German equivalents. If I'm falsely generalising here, feel free to come up with an alternative pair of similar-but-not-identical meanings.
- - - Updated - - -
Already looked at it, does not affect my arguments. You are assuming when you see 0.999... = 1 via geometric series on the web it infers a finite 1. and not 1/1 as a fractional approximation. Googling is not a substitute for reasoning.
Are you now saying that 1.0 and 1/1 are two different numbers too?
