# Thread: >= Nano Trivia <= , or is it?

1. ## Re: >= Nano Trivia <= , or is it?

Al,
I was thinking more of limits used in integration where you think of a limit as say:
The limit of "n", as "n" goes to infinity....which is the same as your last comment.

2. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by MikeC
Al,
I was thinking more of limits used in integration where you think of a limit as say:
The limit of "n", as "n" goes to infinity....which is the same as your last comment.
Yes I figured as much...

3. ## Re: >= Nano Trivia <= , or is it?

Mathematically 10 is greater than 9.9 repeating. But not by much.

In every practical application , 9.9 repeating would get rounded to 10 so then they are considered equal.

4. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by aRob
Mathematically 10 is greater than 9.9 repeating. But not by much.

In every practical application , 9.9 repeating would get rounded to 10 so then they are considered equal.
2 ways to prove that they are in fact equal.

1. On a number line, what value would be between them?

none...

2.
Code:
```         _
10x=99.999
_
x=9.999```
subtract
9x=90

therefore

x=10

5. ## Re: >= Nano Trivia <= , or is it?

:D
Now to remember the 6 line proof for proving 0 does not equal 1 ! (It was right after that when I stopped my math courses!)

6. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by Al Buchholz
2 ways to prove that they are in fact equal.

1. On a number line, what value would be between them?

none...

2.
Code:
```         _
10x=99.999
_
x=9.999```
subtract
9x=90

therefore

x=10
Al:
I have yet to figure out what is the point you are trying to make and my questions went unanswered. You must be in the state of "UN" as the commercial goes. To the best I could glean, I could see couple problems with your comments:

First: You are asking the wrong question and clearly came up with the wrong answer.
Second: Yes, as a matter of accepted principal 9.999.. to infinity equals 10, but to prove that using subtraction is about the worst way to do that in software computing. On paper, yes. In computers, no and let's not get into that, it's a whole new topic altogether.

7. ## Re: >= Nano Trivia <= , or is it?

Guys the answer is indeed 100%
as the Math tends to 100%

8. ## Re: >= Nano Trivia <= , or is it?

Now having ambled through the hypothesis of this debate, I would just add the >= simply removes the doubt. If it is not >= then nothing happens, yet if the programmer gets that one precious decimal wrong in their interpretation of > (and I know we are never wrong so hard to say) it can cost billions.

9. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by ColinJD
Guys the answer is indeed 100%
as the Math tends to 100%
You have already provided an example of a number with out a digit of 8. And there are many more.

So either something was lost in the translation of the question, or the answer - 100% - is incorrect.

10. ## Re: >= Nano Trivia <= , or is it?

If I am understanding the question correctly, then 100% is the correct answer.
It's a trick question.

Between zero and infinity, what percetage of all the decimal number have a digit 8 in them?

Between zero and infinity you could produce any random numbers all of which (not exactly) are decimal by definition, and all of which most definitely will have the digit 8.

I said "not exactly", because all the numbers produced will be decimals with the exception of zero, however that does not count in the grand scheme of things and secondly the question specifically asks what percentage of all the decimal.. thus excluding the zero.
There was a minor typo in the question (number should have been numbers) but it makes no difference.

Please, I sure hope no one is going to start a debate about zero and if zero has decimals, or is a decimal, or if it is an integer etc. Just for the sake of peace, let's leave it alone.

11. ## Re: >= Nano Trivia <= , or is it?

Al,

Looking at proof #1:

If we consider only integers and place them on a number line then there is no space between 9 and 10, thus proving that 9 equals 10. But there is no space between 8 and 9 either so 8=9 and then 8=10 so all integers are equal.

I would say that in fact there exists a number 0.000 ... 0001 which you can add to 9.999 repeating to give 10.

Looking at proof #2:

These are just unrelated equations for variable x. I can set up similar equations :
3x=9 ( so x=3)
2x=4 ( so x=2)
I can subract the two equations 3x-2x=9-4 to get
x=5
Therefore x=2=3=5

The number of numbers between 0 and infinity is infinite. The number of numbers containing an eight is also infinite. The percentage of numbers containing an eight is 100 *(number of numbers containing an eight / number of numbers) which is 100*(infinity/infinity) which is 100%.

12. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by aRob
Al,

Looking at proof #1:

If we consider only integers and place them on a number line then there is no space between 9 and 10, thus proving that 9 equals 10. But there is no space between 8 and 9 either so 8=9 and then 8=10 so all integers are equal.

I would say that in fact there exists a number 0.000 ... 0001 which you can add to 9.999 repeating to give 10.

Looking at proof #2:

These are just unrelated equations for variable x. I can set up similar equations :
3x=9 ( so x=3)
2x=4 ( so x=2)
I can subract the two equations 3x-2x=9-4 to get
x=5
Therefore x=2=3=5

The number of numbers between 0 and infinity is infinite. The number of numbers containing an eight is also infinite. The percentage of numbers containing an eight is 100 *(number of numbers containing an eight / number of numbers) which is 100*(infinity/infinity) which is 100%.
Which proves if you start with a false premise, you can get false results.

False premise 1.

A number line with only integers. Not true, you are mixing ideas.

False premise 2.

You have 2 unequal statements that you are subtracting. Mine are both true

if 3x=9, then 2x=8 is false....

Somewhat like Mike's previous statement about a proof that he couldn't remember where the result is 1=0. The proof is based on a false premise of dividing by zero to get a number.

To make a proof work all steps must be valid and true.

The last one about the infinity, for a concept to be true, all proofs must be true. Sometimes some proofs appear to be true, but another method shows the concept to be something else.

So, since the example showed a number without an 8, the number of numbers with an 8 can't be 100%.

Many times is easier to disprove than to prove.

Maybe we should have a mathematics topic forum... Then we can talk about the different degrees/levels of infinity...

13. ## Re: >= Nano Trivia <= , or is it?

Al,

False premise #1:

I used integers as simplified example of attempting to use a number line to prove something. You can't prove 10=9.999... using a number line.

False premise #2:

You have 2 unequal statements that you are subtracting. Mine are both true

if 3x=9, then 2x=8 is false....
if 10x=99.999... then 9x=90 is false

Your equations are just as false/true as mine are.

14. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by aRob
False premise #2:

if 10x=99.999... then 9x=90 is false

Your equations are just as false/true as mine are.
Based on what?

if

2=2
(multiple both sides of the equation by 10)
then
2x10=2x10
or
20=20
subtract equals from equals
18=18
or
-18=-18

depending on the order that you do it, but the equation is still valid and true.

That's all I did with the variables.

Like this...
http://mathforum.org/dr.math/faq/faq.0.9999.html

15. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by aRob
if 10x=99.999... then 9x=90 is false

Your equations are just as false/true as mine are.
Another way to illustrate Al's logic is as follows:

Suppose: x = 9.999...

Then:
10x = 99.999...
(10x - x) = (99.999... - 9.999...)
9x = 90
x = 10

That's a fully legitimate proof.

Steve

16. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by Steve Andrews
Another way to illustrat Al's logic is as follows:

Suppose: x = 9.999...

Then:
10x = 99.999...
(10x - x) = (99.999... - 9.999...)
9x = 90
x = 10

That's a fully legitimate proof.

Steve
eloquently stated... much clearer than I babbled...

I wish I had invented that proof.. But at least I can copy it...... Ain't Math fun???!!!

17. ## Re: >= Nano Trivia <= , or is it?

Al,

OK, I see how you were doing this.
10x=99.9999...
divide by 10 to get
x=9.9999...
then subtract 10x-x = 99.9999... - 9.9999...
to get
9x=90
so
x=10

Nice, but you lost a digit by doing the division( 99.9999... is infinity long and 9.9999... is only infinity-1 long). It should be accounted for in the subtraction. After all, it's still hanging on to the end of that 99.9999...

10x=99.9999...
divide
x=9.9999...
subtract
9x=90.000...0009
Oh no, now
x>10

Maybe the division added a decimal place ( 99.9999... is infinity long and 9.9999... is infinity+1 long). Still need to account for it.
9x=90 - 0.000...0009
so
x<10

I guess it depends on how long infinity is.

Should I comment on the 100% problem again or leave it?

18. ## Re: >= Nano Trivia <= , or is it?

This debate will never end. It goes to show that no one can possibly comprehend zero nor infinity.
The idea that 9.9999....=10 is based on the "logic" that as you add more decimals the distance between 9.9999... and 10 gets smaller and smaller and since you could add an infinite number of decimals "eventually" the distance becomes zero and if there is no distance between the 2 then they are equal.
Really?
Not really. Mathematicians have come to accept that, but it goes to show that no human mind can comprehend zero much less infinity.
Does the distance ever get to zero?
It defies the First law of Thermokinetics..Here math will conflict with physics when they shouldn't.

But mathematician as a practical matter resolved to accept this when they should have dropped it as unresolved and a "cannot be resolved" matter.
When you come to the gates of Zero and Infinity ... walk, just walk. You simply cannot apply any logic to either, because logic is finite and cannot be applied to infinite matters. Just say: this cannot be resolved, period. And walk.

19. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by aRob
Nice, but you lost a digit by doing the division( 99.9999... is infinity long and 9.9999... is only infinity-1 long). It should be accounted for in the subtraction. After all, it's still hanging on to the end of that 99.9999...

10x=99.9999...
divide
x=9.9999...
subtract
9x=90.000...0009
Oh no, now
x>10

Maybe the division added a decimal place ( 99.9999... is infinity long and 9.9999... is infinity+1 long). Still need to account for it.
9x=90 - 0.000...0009
so
x<10

I guess it depends on how long infinity is.

Should I comment on the 100% problem again or leave it?
No nothing is left hanging..... Perhaps the computer representation of a finite number of digits is confusing the subtraction for you.

Your choice on the 100% of a given digit. But at this point it's probably best to find another authoritative source for the solution explanation... I didn't see it on the Ask Dr. Math site, but I didn't look too hard either...

And G's right about some people don't understand the issues, but that doesn't mean that no one understands it..

20. ## Re: >= Nano Trivia <= , or is it?

This thread that started out with a simple concept turns out to be a debate about infinity.

So as the issue does not get lost in the ever widening debate, I still maintain that:

x>"L"
is a lot better than:
x>="M"

and:
x>{01/01/2009}
is a lot better than:
x>={01/02/2009}

and as to numeric, and hopefully by now everyone came to realize that you cannot store "Infinity" in a field (or a variable) and that you are limited to a certain number of decimals, then all you have to do, assuming that the values you are dealing with are in decimals, is to step back one decimal. For all practical purposes, the majority of all numeric fields use 2 decimals, if any. In few cases you use more. If you use 16 decimals, and if you really rely on the accuracy of the 16th decimals, you have more trouble beyond the scope of this thread.

21. ## Re: >= Nano Trivia <= , or is it?

But why bother worrying about how many decimals when you can just use '>='.

Interesting thought though G but like your thread title states its just trivia and personally I'd advocate business as usual for most scenarios and continue using the '>=' method.

Oh and as far as some of the math go it's a little worrying. I am far from a mathematician but....

(I can't bring myself to use X as it can get confusing with the multiplication symbol)

10Y=99.999

(as G said lets leave infinity alone and give it a fixed number of decimals for calculation purposes)

For 10Y to equal 99.999, Y must equal 9.9999.

Therefore

10x9.9999=99.999

Does everyone agree?

Now,

10Y-Y=99.999-9.9999

and you get

10Y-Y=89.9991 not 90.

Please also note 10Y doesn't equal 89.9991 or even 90. You all seem to be losing that -Y in your equations or -X in you examples. Where did it go?

Like I said maths isn't really my thing and I welcome any corrections to my attempt at making sense of some of these proofs.

Oh and finally I haven't read all the posts in this thread so if I have missed something then my apologises.

22. ## Re: >= Nano Trivia <= , or is it?

gmeredith,

Their proofs are based on the idea that when dealing with infinity, 9.9999... and 99.9999... have the same number of decimal places so when subtracting the two numbers, the decimal part disappears. If you start with a finite number of decimal places,no matter how many, 9.9999..(finite repeat) will always be less than 10.

23. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by gmeredith17
But why bother worrying about how many decimals when you can just use '>='.
Gee.. I don't know. I didn't know that every number in every numeric field must have decimals? Didn't know that you guys use decimals in everything, and if people are having trouble with decimals, how do they manage using them routinely in these fields?! Huh! Sounds like a self-defeating argument.

These are theoretical answers to theoretical questions (really nit-picking questions) because anyone would agree if you have a numeric field incrementing on integer, then logically:
x>9
is better than
x>=10

But some like to loose the big picture and argue the exceptions.

24. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by G Gabriel
anyone would agree if you have a numeric field incrementing on integer, then logically:
x>9
is better than
x>=10

But some like to loose the big picture and argue the exceptions.
The point is that anyone or everyone doesn't agree with that hypothesis and conclusion for a variety of reasons.

Now others have multiple points of view and can determine for themselves what is appropriate.

25. ## Re: >= Nano Trivia <= , or is it?

I have yet to see those "variety of reasons". As long as this thread has gone, haven't seen them yet and don't suppose will ever see them.

This "debate" has reached the point of diminishing returns.. all points to be made have already been made and each can make up their mind or dig their heels.. either way, is no skin off my nose.

26. ## Re: >= Nano Trivia <= , or is it?

if you do not like filter="field >= 10"
what you think about using the .not. operator:

.not.(field<10)

27. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by G Gabriel
I have yet to see those "variety of reasons"
I covered, earlier in the thread, the only "variety of reasons" that matter,
• #1 and foremost, it is not slower, it is exactly the same time to execute in Alpha Five (or just about any other computer or language still in existence). While a useful inquiry, especially if there was any time difference, the answer is 0.0000000 seconds difference in time to execute
• #2. It is logically clearer to developers and other readers of code. Clarity of code is always important, unless you wish to protect your source code through confusion - which almost always backfires when you need to revisit the code 6 months later)
Hi Ron,

Originally Posted by rleunis
if you do not like filter="field >= 10" what you think about using the .not. operator: .not.(field<10)
While a clever solution, it takes longer to execute in Alpha 5, albeit an almost unmeasurable amount, as Alpha's expression evaluation is extremely fast. Most compilers (not the AEX Alpha file code compile which is not really a compile in the computer language sense) in computer languages that do clever compiler optimizations, and one of them would convert .not.(field<10) to field>=10

What really drives coders crazy, is when a compiler sees something called Loop-invariant code motion (often not seen by a coder, or for timing delays) that is really a repetitive operation in the loop, as in
for i =1 to 50
x=10
next
eliminates it to
x=10
I'm absolutely sure Alpha Five's Xbasic does no compiler optimizations at all, as it is primarily an interpreted language. There are times, however, that the expression evaluator seems to do some minor expression optimization in it's execution, most likely Common subexpression elimination, but I have not explicitly checked for this.

But for those looking for speed, it really pays off if you understand the methods of loop optimization (especially loop unrolling), as these can be applied manually for big increases in speed.

28. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by csda1
I covered, earlier in the thread, the only "variety of reasons" that matter,
If that's the best anyone could come up with in opposition,it's pretty lame if you ask me.
As to the first reason, my research on that came empty, so I will take your word for it but, and that goes into the second reason, clarity of code, that comes from clarity of mind which seems lacking with some.

It's a simple logic:
If something is "More than or equal to" something else, then logically it is simply more than the thing immediately before that other thing. If I explain this to my Neighbor's cat, she will get it the first time. It is not that people don't understand that, but for psychological impairments that seem to challenge self-affirmation, they refuse to understand it. Can't help anyone there and getting tired of trying.

29. ## Re: >= Nano Trivia <= , or is it?

Originally Posted by rleunis
if you do not like filter="field >= 10"
what you think about using the .not. operator:

.not.(field<10)
I would if I were a contortionist
.not.(field<10) is the same as field>9
What would you rather use? Assuming of course that the increment is an integer of 1.

30. ## Re: >= Nano Trivia <= , or is it?

You stated: "The point of my question is the implementation of the combined operands ">=" and "<="."

So I thought you did not like combined operands...

That's why I gave you an alternative solution...

The restriction of an integer of 1 was not part of the original post, I think...

Anyway it does not change my post and validity of it, I think.

It's also valid for any numeric value..

"What would you rather use?"

I do not have a bias towards any solution. Just the one which works and is in line with what I feel is right...As long as the result is the same.

I think this indeed rounds it up nicely:
"but for psychological impairments that seem to challenge self-affirmation, they refuse to understand it"

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