Help me understand

Quote from: John Davis on December 13, 2017, 03:51:00 PM

Nothing about what you described, or reality, prohibits this action. You didn't defend - you moved the goalpost.

Redefining addition doesn't magically make 2+2+2=4.
You are now simply doing something else.

It is quite simple, you have a table, you place 2 apples on it (the first group), and then you place 2 more apples on it (the second group).
How many apples in total? 4.
This is a simple fact of addition, 2+2=4.
You magically counting two of them twice to pretend it is 2+2+2 doesn't actually make it 2+2+2. It is still just 2+2.
If you want it to be 2+2+2, then put another 2 apples up, then you end up with 6.

Yeah c'mon John, this is a pretty simple concept, even for me. Can you please stop embarrassing yourself and the entire flat earth collective with this. Boots, we need you man!!

Quote from: Shifter on December 13, 2017, 09:37:35 PM

Every number you could ever string together can be found in pi somewhere.

Do you have any proof of that?

It's infinite. You'll find it somewhere. We have what, calculated it to 5 trillion digits? Pathetic. I'll concede when we get to infinity and there is a combination of numbers that is not in there. Until then (which will be never) I will say that in an infinite string, anything is possible.

Quote from: JackBlack on December 13, 2017, 10:54:42 PM

Quote from: Shifter on December 13, 2017, 09:37:35 PM

Every number you could ever string together can be found in pi somewhere.

Do you have any proof of that?

It's infinite. You'll find it somewhere. We have what, calculated it to 5 trillion digits? Pathetic. I'll concede when we get to infinity and there is a combination of numbers that is not in there. Until then (which will be never) I will say that in an infinite string, anything is possible.

You can make an infinite decimal by writing all of the numbers in base 10 one after the other, except you leave out the digit 9, e.g. 0.1234567810111213141516171812021...
This is a non repeating infinite string, but doesn't have every possible number in it.

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

It's infinite. You'll find it somewhere. We have what, calculated it to 5 trillion digits? Pathetic. I'll concede when we get to infinity and there is a combination of numbers that is not in there. Until then (which will be never) I will say that in an infinite string, anything is possible.

So no proof.

You can easily have an infinite sequence purely from 1s and 0s which do not repeat.
That would be pi in binary notation.
But that would still be a perfectly valid number in decimal notation, it would not repeat, it would be without end.
Yet no where in it would you even find a 2. The only numbers you would find are 1 and 0 and some combinations made of them.

So what you mean is you are making a baseless claim with nothing to back up up.

People have even made pages to try and find sequences in pi, like this one:
http://www.angio.net/pi/
It couldn't even find "5456846215"
Neither could
http://www.subidiom.com/pi/pi.asp
nor
https://www.dcode.fr/pi-digits

This one:
http://www.subidiom.com/pi/pi.asp
appears to have the most digits of the ones I quickly found.
So feel free to try other combinations.
But first, let me know where:
5456846215
appears.

Also you can easily show that 0.999...=1 by the geometric series formula.

Quote from: JackBlack on December 13, 2017, 10:53:35 PM

Quote from: John Davis on December 13, 2017, 03:51:00 PM

Nothing about what you described, or reality, prohibits this action. You didn't defend - you moved the goalpost.

Redefining addition doesn't magically make 2+2+2=4.
You are now simply doing something else.

It is quite simple, you have a table, you place 2 apples on it (the first group), and then you place 2 more apples on it (the second group).
How many apples in total? 4.
This is a simple fact of addition, 2+2=4.
You magically counting two of them twice to pretend it is 2+2+2 doesn't actually make it 2+2+2. It is still just 2+2.
If you want it to be 2+2+2, then put another 2 apples up, then you end up with 6.

Yeah c'mon John, this is a pretty simple concept, even for me. Can you please stop embarrassing yourself and the entire flat earth collective with this. Boots, we need you man!!

I didn't redefine it, a poor example was given and not defended.

Arguing with a round earther is like arguing with a wall.

Quote from: JackBlack on December 13, 2017, 10:54:42 PM

Quote from: Shifter on December 13, 2017, 09:37:35 PM

Every number you could ever string together can be found in pi somewhere.

Do you have any proof of that?

It's infinite. You'll find it somewhere. We have what, calculated it to 5 trillion digits? Pathetic. I'll concede when we get to infinity and there is a combination of numbers that is not in there. Until then (which will be never) I will say that in an infinite string, anything is possible.

This is unknown. People expect this to be true, but there is no proof that I know of. It certainly doesn't follow from the expansion of pi being infinite and non-repeating; for example 0.01001000100001000001... is infinite and non-repeating and does not contain every number as a substring.

 

Quote from: John Davis on December 13, 2017, 08:46:44 PM

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

Haven't I shown the problem with 1.999...9923 here? 

I didn't redefine it, a poor example was given and not defended.

No, a good example was given which you didn't want to accept so you felt the need to lie about it.
You get 2 apples and put them on a table. You then get another 2 and put them on the table.
How many are on the table?
2+2=4.
How does the extra 2 come into it?

Arguing with a round earther is like arguing with a wall.

No, it is like arguing as a wall, where you completely ignore what the REer says and just repeat the same refuted crap/lies.

<< guff totally irrelevant to your flatularism and our globularism deleted >>

You claim, "Arguing with a round earther is like arguing with a wall."

What on earth have your flatularism and our globularism got to do with all the irrelevant stuff you are posting?

I do assume that if you call us globularists you expect to be called flatularists - it seems logical.

Quote from: John Davis on December 14, 2017, 10:24:59 AM

<< guff totally irrelevant to your flatularism and our globularism deleted >>

You claim, "Arguing with a round earther is like arguing with a wall."

What on earth have your flatularism and our globularism got to do with all the irrelevant stuff you are posting?

I do assume that if you call us globularists you expect to be called flatularists - it seems logical.

I think it would be flatist.

Rabinoz, the way you present my point of view is not fair, and you know you are doing it. While I do enjoy discussing a topic before I reach a decision on it, and weigh in on my community when I do so, your attitude and demeanor has been against reason for quite some time. Want to chat, and get to the bottom of this via skype or google hangouts sometime? This atmosphere is aggressive, and I feel it can be dissolved with a little facetime.

And to the bottom of my many digressions too? I get your anger, I just don't find it founded. I'd like to understand.

Quote from: John Davis on December 13, 2017, 08:46:44 PM

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

Can I get a response for this. Mainly for the point about 1.999...9968

Quote from: Empirical on December 14, 2017, 12:47:38 AM

Quote from: John Davis on December 13, 2017, 08:46:44 PM

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

Can I get a response for this. Mainly for the point about 1.999...9968

If the universe turns out to be infinite, that means we're all fractions of infinity, so we are all infinite. WE ARE ALL ALL.

Does that answer your question?

Quote from: Empirical on December 15, 2017, 10:47:40 AM

Quote from: Empirical on December 14, 2017, 12:47:38 AM

Quote from: John Davis on December 13, 2017, 08:46:44 PM

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

Can I get a response for this. Mainly for the point about 1.999...9968

If the universe turns out to be infinite, that means we're all fractions of infinity, so we are all infinite. WE ARE ALL ALL.

Does that answer your question?

We would be infinite fractions of infinity.
Infinity/infinite = indeterminate, so they isn't a problem.
Anyway I would like a response from John Davis.

Quote from: Empirical on December 14, 2017, 12:47:38 AM

Quote from: John Davis on December 13, 2017, 08:46:44 PM

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

Can I get a response for this. Mainly for the point about 1.999...9968

The name isn't confusing unless you use it inconsistently. It sounds like your concern is that it is not Archimedean. Is this right?

Also, we should probably split this math stuff out to the philosophy forums, or at least its own thread. Agreed?

Quote from: Empirical on December 15, 2017, 10:47:40 AM

Quote from: Empirical on December 14, 2017, 12:47:38 AM

Quote from: John Davis on December 13, 2017, 08:46:44 PM

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

Can I get a response for this. Mainly for the point about 1.999...9968

The name isn't confusing unless you use it inconsistently. It sounds like your concern is that it is not Archimedean. Is this right?

I'm unfamiliar with Archimedean in this context.
My concern is that the name "real number" makes it sound like they are somehow more real than other mathematical objects. They is nothing wrong with using number like 1.999...9968, as long as it is given a clear meaning.
So it's wrong to say "you can't use 1.999...9968 because it doesn't exist", but it is currently not fully defined, which it needs to be if it is to be used in a mathematical proof.

Also, we should probably split this math stuff out to the philosophy forums, or at least its own thread. Agreed?

Agreed.

Quote from: John Davis on December 16, 2017, 08:27:21 AM

Quote from: Empirical on December 15, 2017, 10:47:40 AM

Quote from: Empirical on December 14, 2017, 12:47:38 AM

Quote from: John Davis on December 13, 2017, 08:46:44 PM

So its okay to break the rules when it suits you, or convention?

So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.

It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity),  which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.

Can I get a response for this. Mainly for the point about 1.999...9968

The name isn't confusing unless you use it inconsistently. It sounds like your concern is that it is not Archimedean. Is this right?

I'm unfamiliar with Archimedean in this context.
My concern is that the name "real number" makes it sound like they are somehow more real than other mathematical objects. They is nothing wrong with using number like 1.999...9968, as long as it is given a clear meaning.
So it's wrong to say "you can't use 1.999...9968 because it doesn't exist", but it is currently not fully defined, which it needs to be if it is to be used in a mathematical proof.

I agree with this. I also agree we shouldn't be using the term 'real number' as we are. I feel like we've used it 3 different ways so far aside from the commonly accepted definition of a Real number.

I offered earlier to attempt to define it a bit more discretely; if I have some time past my dev work this weekend I'll attempt to do so in a reasonable way here.