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The limits of our counting system

natoast
Posts: 204
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3/28/2013 2:34:38 PM
Posted: 3 years ago
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1. But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?
The_Fool_on_the_hill
Posts: 6,071
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3/28/2013 2:53:50 PM
Posted: 3 years ago
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1. But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

The Fool: You are conflating symbolization limits, with conceptual.
"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
Sidewalker
Posts: 3,713
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3/28/2013 3:54:43 PM
Posted: 3 years ago
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

It's equal to 1, so it dosn't matter.

Proof:
1/9 = .111...
9 * 1/9 = .999...
1 = .999...

http://en.wikipedia.org......

.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
natoast
Posts: 204
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3/28/2013 4:53:03 PM
Posted: 3 years ago
At 3/28/2013 3:54:43 PM, Sidewalker wrote:
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

It's equal to 1, so it dosn't matter.

Proof:
1/9 = .111...
9 * 1/9 = .999...
1 = .999...

http://en.wikipedia.org......

How do you know that 1/0 is equal to .111 ...?
Sidewalker
Posts: 3,713
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3/30/2013 7:32:15 AM
Posted: 3 years ago
At 3/28/2013 4:53:03 PM, natoast wrote:
At 3/28/2013 3:54:43 PM, Sidewalker wrote:
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

It's equal to 1, so it dosn't matter.

Proof:
1/9 = .111...
9 * 1/9 = .999...
1 = .999...

http://en.wikipedia.org......

How do you know that 1/0 is equal to .111 ...?

I presume you mean 1/9 not 1/0, and the reason I know it is because I can understand and do simple division.

As far as mathematics is concerned, proofs are pretty convincing, it's a simple fact that 1 = .999...
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
ConservativePolitico
Posts: 8,210
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3/30/2013 11:05:51 AM
Posted: 3 years ago
At 3/28/2013 3:54:43 PM, Sidewalker wrote:
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

It's equal to 1, so it dosn't matter.

Proof:
1/9 = .111...
9 * 1/9 = .999...
1 = .999...

http://en.wikipedia.org......



.

Just because your calculator rounds .999 repeating to 1 doesn't mean it equals 1.
Sidewalker
Posts: 3,713
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3/30/2013 11:45:33 AM
Posted: 3 years ago
At 3/30/2013 11:05:51 AM, ConservativePolitico wrote:
At 3/28/2013 3:54:43 PM, Sidewalker wrote:
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

It's equal to 1, so it dosn't matter.

Proof:
1/9 = .111...
9 * 1/9 = .999...
1 = .999...

http://en.wikipedia.org......



.

Just because your calculator rounds .999 repeating to 1 doesn't mean it equals 1.

That's a non-sequitur of course.

It equals 1 by definition, and there are several mathematical proofs of tht fact, it isn't refuted just because you don't understand it.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
natoast
Posts: 204
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3/31/2013 12:17:55 PM
Posted: 3 years ago
At 3/30/2013 7:32:15 AM, Sidewalker wrote:
At 3/28/2013 4:53:03 PM, natoast wrote:
At 3/28/2013 3:54:43 PM, Sidewalker wrote:
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

It's equal to 1, so it dosn't matter.

Proof:
1/9 = .111...
9 * 1/9 = .999...
1 = .999...

http://en.wikipedia.org......

How do you know that 1/0 is equal to .111 ...?

I presume you mean 1/9 not 1/0, and the reason I know it is because I can understand and do simple division.

You can do simple division? I can prove a finite series of decimals is equal to a fraction easily because of the definition of a fraction (.1 equals 1/10) so 1/5 is .2 because 5 goes into ten twice. But how many times does 9 go into 10? It goes on forever. I'm not sure it's possible to prove 1/9 is equal to .111.

As far as mathematics is concerned, proofs are pretty convincing, it's a simple fact that 1 = .999
Sidewalker
Posts: 3,713
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3/31/2013 7:01:30 PM
Posted: 3 years ago
At 3/31/2013 12:17:55 PM, natoast wrote:
At 3/30/2013 7:32:15 AM, Sidewalker wrote:
At 3/28/2013 4:53:03 PM, natoast wrote:
At 3/28/2013 3:54:43 PM, Sidewalker wrote:
At 3/28/2013 2:34:38 PM, natoast wrote:
I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

It's equal to 1, so it dosn't matter.

Proof:
1/9 = .111...
9 * 1/9 = .999...
1 = .999...

http://en.wikipedia.org......

How do you know that 1/0 is equal to .111 ...?

I presume you mean 1/9 not 1/0, and the reason I know it is because I can understand and do simple division.

You can do simple division?

Yeah, most people learn it in grade school.

I can prove a finite series of decimals is equal to a fraction easily because of the definition of a fraction (.1 equals 1/10) so 1/5 is .2 because 5 goes into ten twice.

OK

But how many times does 9 go into 10?

1.111... simple division again.

It goes on forever. I'm not sure it's possible to prove 1/9 is equal to .111.

Sure it is, you only need to understand simple division, the decimal is a simple repeating decimal.

Do you really think solving for 1/3 is impossible? There is something unresolvably complex about a simple repeating decimal? Really?

I'm pretty sure most fifth graders understand it.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
AlbinoBunny
Posts: 3,781
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4/4/2013 9:21:06 AM
Posted: 3 years ago
It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...
3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.4
3/3 = 1.
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Sidewalker
Posts: 3,713
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4/4/2013 11:33:22 AM
Posted: 3 years ago
At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:
It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...
3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.4
3/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...
it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
AlbinoBunny
Posts: 3,781
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4/4/2013 11:41:28 AM
Posted: 3 years ago
At 4/4/2013 11:33:22 AM, Sidewalker wrote:
At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:
It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...
3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.4
3/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...
it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..

In base twelve a third is written as 0.4. Base twelve makes mathematics easier. Yes, it is still the same amount, it's just easier to use in equations.
bladerunner060 | bsh1 , 2014! Presidency campaign!

http://www.debate.org...
http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

May the best man win!
Sidewalker
Posts: 3,713
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4/4/2013 4:43:50 PM
Posted: 3 years ago
At 4/4/2013 11:41:28 AM, AlbinoBunny wrote:
At 4/4/2013 11:33:22 AM, Sidewalker wrote:
At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:
It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...
3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.4
3/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...
it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..

In base twelve a third is written as 0.4. Base twelve makes mathematics easier. Yes, it is still the same amount, it's just easier to use in equations.

Yes, but in base twelve 1/5 and 1/7 are repeating decimals, a base twelve counting system does not does not give a finite representation for all fractions so it just doesn't solve the problem of repeating decimals. There might be fewer repeating decimals, but you still have them.

Plus, I really don't think it's all that practical to change the worldwide counting system, especially since you might just be the only person in the world that thinks a duodecimal system is "just easier".
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
AlbinoBunny
Posts: 3,781
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4/5/2013 3:03:34 AM
Posted: 3 years ago
At 4/4/2013 4:43:50 PM, Sidewalker wrote:
At 4/4/2013 11:41:28 AM, AlbinoBunny wrote:
At 4/4/2013 11:33:22 AM, Sidewalker wrote:
At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:
It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...
3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.4
3/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...
it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..

In base twelve a third is written as 0.4. Base twelve makes mathematics easier. Yes, it is still the same amount, it's just easier to use in equations.

Yes, but in base twelve 1/5 and 1/7 are repeating decimals, a base twelve counting system does not does not give a finite representation for all fractions so it just doesn't solve the problem of repeating decimals. There might be fewer repeating decimals, but you still have them.

Plus, I really don't think it's all that practical to change the worldwide counting system, especially since you might just be the only person in the world that thinks a duodecimal system is "just easier".

There are less repeating "decimals" and more shorter "decimals" as well. And the multiplications are easier. It also works better with any multiple of two, three or either. I'm not the only person, once you get used to it it's easier. If you taught it in parallel with decimal to kids they'd probably wonder why we use decimal. The gains aren't huge, but when compounded it's enough to consider whether it should be used in parallel with decimal.
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http://www.debate.org...
http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

May the best man win!