1 is 0.9999999999999............

Tach said:
But "we" don't. For good reason.

We do though. 0 = 0.0 = 00.00 = ... = (0)*.(0)*.
We don't write leading zeros, and we don't write trailing zeros for finite numbers, but they're still there.
 
We do though. 0 = 0.0 = 00.00 = ... = (0)*.(0)*.

Well, you seem to share the same fringe views with Undefined , then. No wonder that you were so eager to agree with him when he "corrected" you. The irony is that you got it initially right, only to correct yourself the wrong way. :D

We don't write leading zeros, and we don't write trailing zeros for finite numbers, but they're still there.

No, no one in his right mind writes leading zeroes. For good reason, for ANY numbers.
But this is not the original debate, this is just a diversion from the original debate. The original debate was caused by the insertion of zeroes to the right of the decimal point, remember? This new thing with "leading zeroes" is just another one of Undefined's diversions when he's shown to be wrong, so why do you play into his hand?
 
Tach said:
No, no one in his right mind writes leading zeroes. For good reason, for ANY numbers.
Now you're just being stupid.

Are you really sure that 9.0 is not equal to 09.0, or 009.0, or perhaps it's not equal to 0009.0000 either? Are you saying writing a number that way means you aren't "in your right mind"?

As I said, we don't write leading or trailing zeros.
What kind of mind would you require in order to prove there aren't any zeros there? Would this proof ahow that 9.0 and 09.00 are different numbers?
 
...
No, no one in his right mind writes leading zeroes. For good reason, for ANY numbers.
But this is not the original debate, this is just a diversion from the original debate. The original debate was caused by the insertion of zeroes to the right of the decimal point, remember? This new thing with "leading zeroes" is just another one of Undefined's diversions when he's shown to be wrong, so why do you play into his hand?

Read in full context so far please, Tach.

If you write a decimal FRACTION string value for the ratio 9/10 measurement/analytical 'result', you can write .9 or 0.9 or .90 or .900 or etc, depending on what 'accuracy/precision' of measurement result/process you wish to convey to whomever reads that 'value' result of that measurement 'degree of precision/accuracy' applied by the measurement/analytical method/construct. Yes?

And when you write a decimal FRACTIONAL string value for a ratio 9/100 'measurement result', you can write .09 or 0.09 or .090 or 0.090 or 0.0900 or etc, again for conveying the degree of measurement precision accuracy and value employed to arrive at that fractional result. Yes?

Now, more importantly, do you see the crucial role of the ACTIVE leading 0 when the decimal fractional string MUST include the LEADING ZERO in order to make the value 9/100ths in decimal format?

Do you see that if you left out that leading 0, it would be 9/10ths! not 9/100ths value. Different values when leading zeros are written in for the decimal fractional string values, yes?

Please just think about that and read/understand in context, and then you will see that your leading/trailing zeros "blanket assertions" and "corrections" are not tenable in the context. Thanks.
 
Now you're just being stupid.

Talking to yourself in the mirror again?

Are you really sure that 9.0 is not equal to 09.0, or 009.0, or perhaps it's not equal to 0009.0000 either? Are you saying writing a number that way means you aren't "in your right mind"?

Of course that they are equal, this is not what I objected to. What I objected to is your singing the same tune as Undefined. Maybe you two are not so different after all.

But this is not the original debate, this is just a diversion from the original debate. The original debate was caused by the insertion of zeroes to the right of the decimal point, remember? This new thing with "leading zeroes" is just another one of Undefined's diversions when he's shown to be wrong, so why do you play into his hand?
 
Read in full context so far please, Tach.

If you write a decimal FRACTION string value for the ratio 9/10 measurement/analytical 'result', you can write .9 or 0.9 or .90 or .900 or etc, depending on what 'accuracy/precision' of measurement result/process you wish to convey to whomever reads that 'value' result of that measurement 'degree of precision/accuracy' applied by the measurement/analytical method/construct. Yes?

Nope, what you write is 0.9. You have to live with the facts.


And when you write a decimal FRACTIONAL string value for a ratio 9/100 'measurement result', you can write .09 or 0.09 or .090 or 0.090 or 0.0900 or etc, again for conveying the degree of measurement precision accuracy and value employed to arrive at that fractional result. Yes?

Nope, normal people write 0.09. OK, mate?

Now, do you see the importance of the ACTIVE leading 0 when the decimal fractional string MUST include the LEADING ZERO in order to make the value 9/100ths in decimal format?

There isn't any, mate.


Do you see that if you left out that leading 0, it would be 9/10ths! not 9/100ths value. Different values when leading zeros are written in for the decimal fractional string values, yes?

But this is not the original debate, this is just a diversion from the original debate. The original debate was caused by the insertion of zeroes to the right of the decimal point, remember? This new thing with "leading zeroes" is just another one of your diversions when you've been shown to be wrong, get it, mate?
 
Nope, what you write is 0.9. You have to live with the facts.




Nope, normal people write 0.09. OK, mate?

Undefined said:
Now, more importantly, do you see the crucial role of the ACTIVE leading 0 when the decimal fractional string MUST include the LEADING ZERO in order to make the value 9/100ths in decimal format?

There isn't any, mate.




But this is not the original debate, this is just a diversion from the original debate. The original debate was caused by the insertion of zeroes to the right of the decimal point, remember? This new thing with "leading zeroes" is just another one of your diversions when you've been shown to be wrong, get it, mate?

In that (my red highlighting) response from you above, you effectively assert that when writing 0.09 there is no leading zero to distinguish that from 0.9 ??!!

Amazing.

And you (who claim to be an "experimental physicist") do not know that the inclusion of leading/trailing zeros is also a means/convention of/for quickly and effectively indicating/conveying to the reader additional information regarding the specific level/degree of precision/accuracy the measurement was made to?

Amazing.


What is there left to say, except....????!!!!
 
In that (my red highlighting) response from you above, you effectively assert that when writing 0.09 there is no leading zero to distinguish that from 0.9 ??!!

You reading and comprehension skills are as bad as your math skills. Enjoy beating up your newly created strawman.
 
Tach said:
What I objected to is your singing the same tune as Undefined. Maybe you two are not so different after all.
I only made the point that although we don't "normally" write leading zeros to the left of significant digits or trailing zeros to the right of fractions, they're still "there".
It's a valid, if somewhat trivial matter.

So where does "singing the same tune" as Undefined come from? Your desperate need to put other people down?

And this is my initial uncorrected post: if you have a number like 0.999 and multiply it by 10[sup]-2[/sup], the result is 0.00999, the single zero on the left of the decimal point must really be like a string of zeros extending infinitely to the right (which is inductively true since we can multiply by 10-2 indefinitely)

And as Undefined pointed out, this single zero must extend to the left (it's the same as an infinite string), since it's on the left of the decimal point, not the right. So 0.d = (0)*.d, means there is an infinite string of zeros on the left of the decimal point, or on the left of the first nonzero digit. If the decimal point is where you start from, how does it make sense to say this string of zeros extends to the right?
As I also noted, you need to be careful about left and right, and of what. So your objection amounts to you not reading things too closely, or perhaps you're suffering from selective blondness.
 
I only made the point that although we don't "normally" write leading zeros to the left of significant digits or trailing zeros to the right of fractions, they're still "there".
It's a valid, if somewhat trivial matter.

...and I pointed out that no one does that , in practice.

So where does "singing the same tune" as Undefined come from? Your desperate need to put other people down?

It comes from the fact that you are repeating the same trivialities as Undefined. <shrug> . It comes from getting things initially right and then switching your tune to his tune after he "corrected" you.
 
Tach said:
...and I pointed out that no one does that , in practice.
Which has no real bearing on the mathematics, since 0 = 00 = 000 = ..., is true regardless of what people do in practice.

It comes from getting things initially right and then switching your tune to his tune after he "corrected" you.
So you're still claiming that 0.d has a string of zeros extending infinitely to the right? Of what, may I ask?
 
So you're still claiming that 0.d has a string of zeros extending infinitely to the right? Of what, may I ask?

No, you either don't get your error or you pretend that you don't. Let's try again: when you multiplied 0.9 with $$10^{-2}$$ and you obtained 0.009, in what direction did the zeroes extend from the decimal point?
You initially answered it correctly (to the right) but after Undefined bullied you a little , you switched to the wrong answer.
 
Tach said:
Let's try again: when you multiplied 0.9 with and you obtained 0.009, in what direction did the zeroes extend from the decimal point?
They extend to the right of the decimal point, of course.

But since I was referring to the single zero on the left of the decimal point, my corrected statement stands, and Undefined was also therefore correct to point out the mistake I made. You're flogging a dead horse.
 
No, no one in his right mind writes leading zeroes. For good reason, for ANY numbers.

I can think of a number of instances where this is untrue, and here's one:

Windows, when it sorts files by name, sorts them alphabetically so if you have the following list:

File 1, File 2, File 3, File 4, File 5, File 6, File 7, File 8, File 9, File 10, File 11, File 12, File 13, File 14, File 15, File 16, File 17, File 18, File 19, File 20, File 21, File 22, File 23, File 24, File 25.

Windows sorts it thusly:

File 1, File 10, File 11, File 12, File 13, File 14, File 15, File 16, File 17, File 18, File 19, File 2, File 20, File 21, File 22, File 23, File 24, File 25, File 3, File 4, File 5, File 6, File 7, File 8, File 9.

Because that is the correct way of sorting files alphabetically. The only way to get around this is to use leading zeroes. If you do it thusly:

File 01, File 02, File 03, File 04, File 05, File 06, File 07, File 08, File 09, File 10, File 11, File 12, File 13, File 14, File 15, File 16, File 17, File 18, File 19, File 20, File 21, File 22, File 23, File 24, File 25.

If you've got 1000 files, then you need to start with 0001 - the point here being that when it comes to the purposes of sorting, leading zeroes can become significant. Something that, I imagine, is going to stick in your craw as much as it will Undefineds.
 
They extend to the right of the decimal point, of course.

Excellent, so your initial answer was right. Which makes your reversal, under Undefined's tutelage, wrong.

But since I was referring to the single zero on the left of the decimal point, my corrected statement stands, and Undefined was also therefore correct to point out the mistake I made. You're flogging a dead horse.

Let's try a simple exercise. Start with 0.n

1. Multiply be $$10^{-1}$$. You get 0.0n, right? In what direction from the decimal point did zero propagate? (hint: you were taught the answer in 5-th grade)
2. Multiply again by $$10^{-1}$$. You get 0.00n, right? In what direction from the decimal point did zero propagate?
 
I can think of a number of instances where this is untrue, and here's one:

Windows, when it sorts files by name, sorts them alphabetically so if you have the following list:

File 1, File 2, File 3, File 4, File 5, File 6, File 7, File 8, File 9, File 10, File 11, File 12, File 13, File 14, File 15, File 16, File 17, File 18, File 19, File 20, File 21, File 22, File 23, File 24, File 25.

Windows sorts it thusly:

File 1, File 10, File 11, File 12, File 13, File 14, File 15, File 16, File 17, File 18, File 19, File 2, File 20, File 21, File 22, File 23, File 24, File 25, File 3, File 4, File 5, File 6, File 7, File 8, File 9.

Because that is the correct way of sorting files alphabetically. The only way to get around this is to use leading zeroes. If you do it thusly:

File 01, File 02, File 03, File 04, File 05, File 06, File 07, File 08, File 09, File 10, File 11, File 12, File 13, File 14, File 15, File 16, File 17, File 18, File 19, File 20, File 21, File 22, File 23, File 24, File 25.

If you've got 1000 files, then you need to start with 0001 - the point here being that when it comes to the purposes of sorting, leading zeroes can become significant. Something that, I imagine, is going to stick in your craw as much as it will Undefineds.

We were talking arithmetic, as in multiplying with $$10^{-n}$$ , not file naming conventions. Did you miss that?
 
Tach said:
Let's try a simple exercise. Start with 0.n

1. Multiply be $$10^{-1}$$. You get 0.0n, right? In what direction from the decimal point did zero propagate? (hint: you were taught the answer in 5-th grade)
2. Multiply again by $$10^{-1}$$. You get 0.00n, right? In what direction from the decimal point did zero propagate?

But this is about zeros on the right of the decimal point, not the left. The 0 in 0.9 is still equivalent to an infinite string of zeros, and my corrected statement still stands.
It stands, because it's (also) true when you don't divide the number by 10s.

FS.
 
But this is about zeros on the right of the decimal point, not the left.


..as in your post that started to controversy. The one that you answered initially right only to switch to the wrong answer.



The 0 in 0.9 is still equivalent to an infinite string of zeros, and my corrected statement still stands.


This is a different issue, trivially correct but can you stick to the point and not resort to diversions? One issue at a time. Do you agree that the zeroes inserted by the multiplication of 0.n by $$10^{-m}$$ extend to the right, from the decimal point? Yes or no?
 
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