James S Saint wrote:Yeah .. just a matter of recycling on the evens or recycling on the odds.Carleas wrote:... in base 10 is .111... in base 3.
My point still stands... 3 is an even number in base 3
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James S Saint wrote:Yeah .. just a matter of recycling on the evens or recycling on the odds.Carleas wrote:... in base 10 is .111... in base 3.
Ecmandu wrote:You could then argue that the divisor of base and its multipliers are "even"
Carleas wrote:Ecmandu wrote:You could then argue that the divisor of base and its multipliers are "even"
Sure, if you change the definition of 'even', then you could get any result you want. But that's not usually how we think of it (5 isn't even in base 10, even though it's also a prime factor of 10).
No matter the base, numbers that have 2 as a factor continue to have 2 as a factor. And changing the base doesn't affect the properties of odd and even numbers under arithmetic operations.
Ecmandu wrote:In base 3, 2 and 2 add to higher than base, 2 cannot be the lowest common denominator, it has to be 3 or multiples of 3
Ecmandu wrote:division is inverse to multiplication, yet has very strange properties relative to the inverse of addition and subtraction.
So, my question is... why?
Carleas wrote:Ecmandu wrote:In base 3, 2 and 2 add to higher than base, 2 cannot be the lowest common denominator, it has to be 3 or multiples of 3
I don't disagree, but that isn't what "even" means. 2 is still even in base 3.Ecmandu wrote:division is inverse to multiplication, yet has very strange properties relative to the inverse of addition and subtraction.
So, my question is... why?
You're looking at "whole" numbers, by which I take you to mean either integers. And you're right that there's an asymmetry between multiplication and division there: multiply two integers and you always get an integer, divide one integer by another and you don't necessarily get another integer. But you can look at larger and smaller sets of numbers. If you look at just the natural numbers, you see a similar asymmetry between addition and subtraction: add two natural numbers and you always get a natural number, but 3-5 is not a natural number.
Conversely, the rational numbers are closed on division (except for zero), as are the real numbers.
I'm not sure if there are any sets that are closed under division but not multiplication, or subtraction but not addition.
Ecmandu wrote:There's an even finer point to this mystery that is often overlooked. When you place a bar over the 3 to signify its rational repetition, the threes actually regress, technically, at no point are those 3's actually repeating!!
You seem to think that just because you have learned how to divide into decimals that you actually understand why some numbers terminate and others infinitely regress. I assure you, you have no clue.
This doesn't converge.What does 999999999... eventually equal??
But this does converge.But!! Somehow, it makes perfect sense to you that 0.999999... equals 1????
phyllo wrote:This doesn't converge.What does 999999999... eventually equal??But this does converge.But!! Somehow, it makes perfect sense to you that 0.999999... equals 1????
There is no space and no time in mathematics. The concepts of 'when' and 'where' do not apply as you seem to think that they do.If so where does it terminate ?
If not, where does it converge?
Huh? At infinity??
Where exactly is infinity??
Show it to me.
Series which converge add ever smaller numbers to the total until ultimately they add nothing more. That's the basic concept. It's nothing mysterious or inaccessible. One can see it by preforming many calculations on a computer.It actually makes more sense for expansions to converge than contractions...
I'm curious why you think a contraction converges, and how...
phyllo wrote:Series which converge add ever smaller numbers to the total until ultimately they add nothing more. That's the basic concept. It's nothing mysterious or inaccessible. One can see it by preforming many calculations on a computer.
The results are confirmed by other methods. The 0.999... =1 result can be achieved by series expansions or with straight divisions, multiplications, additions and subtractions - probably a dozen have been shown in this thread. In order to accept "your logic", we would have to throw out the work in many fields of mathematics.James S Saint wrote:phyllo wrote:Series which converge add ever smaller numbers to the total until ultimately they add nothing more. That's the basic concept. It's nothing mysterious or inaccessible. One can see it by preforming many calculations on a computer.
That is the fallacy in your reasoning.
There is no point where "ultimately they add nothing more". That point, "at infinity", is erroneous imagining.
It is not.First, math is the abstraction of space and time.
phyllo wrote:It is not.First, math is the abstraction of space and time.
Mathematics can be used to model time and space.
You're confusing space and time and thoughts about space and time - reality and representations of reality.Intetesting... what does mathematics model without time and space? Thoughts are discrete ... what does math model without thought?
phyllo wrote:You're confusing space and time and thoughts about space and time - reality and representations of reality.Intetesting... what does mathematics model without time and space? Thoughts are discrete ... what does math model without thought?
phyllo wrote:Light moves in space. Does thought move in space? From where to where?
Okey-dokeyTechnically it's a trick question... thought can make light move faster... thought can traverse all space and time much faster than light, practically speaking.... you can talk to embodied beings in their state that was trillions upon trillions of light years ago
Or even what they are now... thought moves faster than anything in existence
phyllo wrote:Okey-dokeyTechnically it's a trick question... thought can make light move faster... thought can traverse all space and time much faster than light, practically speaking.... you can talk to embodied beings in their state that was trillions upon trillions of light years ago
Or even what they are now... thought moves faster than anything in existence
Yeah, unfortunately I have to work within my limits. I have never talked to God or spirits or demons, been to heaven or hell, touched infinity, had out of body experiences, been reincarnated, been one with the universal consciousness, made a perpetual motion machine, circumvented the laws of thermodynamics ...*shrug*. Analogies and metaphors have their limits... experience reigns supreme still. So tell me, this infinity that you hang out at where all these series converge for you... is it fun? Oh, that's right... it's just a metaphor! Like I said, experience reigns supreme...
phyllo wrote:Yeah, unfortunately I have to work within my limits. I have never talked to God or spirits or demons, been to heaven or hell, touched infinity, had out of body experiences, been reincarnated, been one with the universal consciousness, made a perpetual motion machine, circumvented the laws of thermodynamics ...*shrug*. Analogies and metaphors have their limits... experience reigns supreme still. So tell me, this infinity that you hang out at where all these series converge for you... is it fun? Oh, that's right... it's just a metaphor! Like I said, experience reigns supreme...
I'm making lemonade with the lemons that I have gathered over the years.
Ecmandu wrote:phyllo wrote:Yeah, unfortunately I have to work within my limits. I have never talked to God or spirits or demons, been to heaven or hell, touched infinity, had out of body experiences, been reincarnated, been one with the universal consciousness, made a perpetual motion machine, circumvented the laws of thermodynamics ...*shrug*. Analogies and metaphors have their limits... experience reigns supreme still. So tell me, this infinity that you hang out at where all these series converge for you... is it fun? Oh, that's right... it's just a metaphor! Like I said, experience reigns supreme...
I'm making lemonade with the lemons that I have gathered over the years.
Well... sounds to me like you're off to a good start.
When these things do occur, try not to go insane like I did!
I'll tell you something very important to keep with you...
The question of whether there is a grand creator, is actually yours to decide. There isn't a wrong answer.
That's how big this cosmos actually is
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