Hilbert original idea of an infinite hotel was manipulated by the
infinite cardinals and set guys including Hilbert.(ZFC)
His original thought of moving guest 1 to room 2 and beyond
for the first 10 guest and then --->oo did not fit the bill
for infinite set theory.
rm# guest#
... ...
10 1
9 2
8 3
7 4
6 5
5 6
4 7
3 8
2 9
1 10

That did not fit into the scheme of infinite sets.
So they manipulated the idea using sets of guest coming into
the hotel and also pairing the rooms off with that idea.
My idea of an --->oo pyramid hotel is based on Hilbert's
original idea in building the room structure bottom up
forming a pyramid hotel. Moving each guest up one room to
accommodated the new incoming guest. Each new line drawn is
guest #1 turning the light on in that room and all newer guest
behind him just move into a lighted room. Guest # 1 will never enter
a lighted room. Keeping with the idea of never retracing a line.
The infinite set guys did come up with a pyramid type hotel to
fit into their scheme but pairing the rooms top down. My pyramid
hotel is just the reverse building rooms outward and bottom up.
Where -x --->oo and x --->oo and y --->oo
Their manipulated version of a pyramid hotel is below.

From Wikipedia
This pairing function can be demonstrated visually by
structuring the hotel as a one-room-deep, infinitely
tall pyramid. The pyramid's topmost row is a single room
: room 1; its second row is rooms 2 and 3;and so on.

Where my pyramid hotel, also 1 room deep, starts at the bottom of
the pyramid where room 1 is x=0 and is built outward in both
directions -x\+x and upward +y forming a continuous 180 degree
pyramid --->oo. Each line representing a room that guest #1 turns on.
In my pyramid there can be no pairing but will --->oo in all 180
degrees which I believe is the limit even for set theory.

Just my thoughts about infinite sets and cardinals are not possible
with this pyramid below.
Any example that would work for ZFC is welcome.

Here is the data for the pyramid again so observing this in real
time is helpful in getting my thoughts across.

Run using Chris's algorithm and set size @ 0.05 and time 50

http://fractallife247.com/test/cmd_plot/

RULDLURULDLDRDLULURURURDRDRDLDRURULULULULDLDLDLDRDLULURURURURURDRDRDRDRDLDRURULULULULULULDLDLDLDLDLDRDLULURURURURURURURDRDRDRDRDRDRDLDRURULULULULULULULULDLDLDLDLDLDLDLDRDLULURURURURURURURURURDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULU LULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRD RDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULU

Here @ Dan's infinite pyramid hotel the first guest will always leave a light on for you. ;=)

On 8/17/2023 1:42 PM, Dan joyce wrote:
>
> Hilbert original idea of an infinite hotel was manipulated by the
> infinite cardinals and set guys including Hilbert.(ZFC)
> His original thought of moving guest 1 to room 2 and beyond
> for the first 10 guest and then --->oo did not fit the bill
> for infinite set theory.
> rm# guest#
> ... ...
> 10 1
> 9 2
> 8 3
> 7 4
> 6 5
> 5 6
> 4 7
> 3 8
> 2 9
> 1 10
>
> That did not fit into the scheme of infinite sets.
> So they manipulated the idea using sets of guest coming into
> the hotel and also pairing the rooms off with that idea.
> My idea of an --->oo pyramid hotel is based on Hilbert's
> original idea in building the room structure bottom up
> forming a pyramid hotel. Moving each guest up one room to
> accommodated the new incoming guest. Each new line drawn is
> guest #1 turning the light on in that room and all newer guest
> behind him just move into a lighted room. Guest # 1 will never enter
> a lighted room. Keeping with the idea of never retracing a line.
> The infinite set guys did come up with a pyramid type hotel to
> fit into their scheme but pairing the rooms top down. My pyramid
> hotel is just the reverse building rooms outward and bottom up.
> Where -x --->oo and x --->oo and y --->oo
> Their manipulated version of a pyramid hotel is below.
>
> From Wikipedia
> This pairing function can be demonstrated visually by
> structuring the hotel as a one-room-deep, infinitely
> tall pyramid. The pyramid's topmost row is a single room
> : room 1; its second row is rooms 2 and 3;and so on.
>
> Where my pyramid hotel, also 1 room deep, starts at the bottom of
> the pyramid where room 1 is x=0 and is built outward in both
> directions -x\+x and upward +y forming a continuous 180 degree
> pyramid --->oo. Each line representing a room that guest #1 turns on.
> In my pyramid there can be no pairing but will --->oo in all 180
> degrees which I believe is the limit even for set theory.
>
> Just my thoughts about infinite sets and cardinals are not possible
> with this pyramid below.
> Any example that would work for ZFC is welcome.
>
> Here is the data for the pyramid again so observing this in real
> time is helpful in getting my thoughts across.
>
> Run using Chris's algorithm and set size @ 0.05 and time 50
>
> http://fractallife247.com/test/cmd_plot/
[snip commands]
> Here @ Dan's infinite pyramid hotel the first guest will always leave a light on for you. ;=)

I think I got it:

https://i.ibb.co/Yj8hMmP/image.png

I don't think there are any copy-and-paste error shit. ;^)

On Thursday, August 17, 2023 at 5:20:31 PM UTC-4, Chris M. Thomasson wrote:
> On 8/17/2023 1:42 PM, Dan joyce wrote:
> >
> > Hilbert original idea of an infinite hotel was manipulated by the
> > infinite cardinals and set guys including Hilbert.(ZFC)
> > His original thought of moving guest 1 to room 2 and beyond
> > for the first 10 guest and then --->oo did not fit the bill
> > for infinite set theory.
> > rm# guest#
> > ... ...
> > 10 1
> > 9 2
> > 8 3
> > 7 4
> > 6 5
> > 5 6
> > 4 7
> > 3 8
> > 2 9
> > 1 10
> >
> > That did not fit into the scheme of infinite sets.
> > So they manipulated the idea using sets of guest coming into
> > the hotel and also pairing the rooms off with that idea.
> > My idea of an --->oo pyramid hotel is based on Hilbert's
> > original idea in building the room structure bottom up
> > forming a pyramid hotel. Moving each guest up one room to
> > accommodated the new incoming guest. Each new line drawn is
> > guest #1 turning the light on in that room and all newer guest
> > behind him just move into a lighted room. Guest # 1 will never enter
> > a lighted room. Keeping with the idea of never retracing a line.
> > The infinite set guys did come up with a pyramid type hotel to
> > fit into their scheme but pairing the rooms top down. My pyramid
> > hotel is just the reverse building rooms outward and bottom up.
> > Where -x --->oo and x --->oo and y --->oo
> > Their manipulated version of a pyramid hotel is below.
> >
> > From Wikipedia
> > This pairing function can be demonstrated visually by
> > structuring the hotel as a one-room-deep, infinitely
> > tall pyramid. The pyramid's topmost row is a single room
> > : room 1; its second row is rooms 2 and 3;and so on.
> >
> > Where my pyramid hotel, also 1 room deep, starts at the bottom of
> > the pyramid where room 1 is x=0 and is built outward in both
> > directions -x\+x and upward +y forming a continuous 180 degree
> > pyramid --->oo. Each line representing a room that guest #1 turns on.
> > In my pyramid there can be no pairing but will --->oo in all 180
> > degrees which I believe is the limit even for set theory.
> >
> > Just my thoughts about infinite sets and cardinals are not possible
> > with this pyramid below.
> > Any example that would work for ZFC is welcome.
> >
> > Here is the data for the pyramid again so observing this in real
> > time is helpful in getting my thoughts across.
> >
> > Run using Chris's algorithm and set size @ 0.05 and time 50
> >
> > http://fractallife247.com/test/cmd_plot/
> [snip commands]
> > Here @ Dan's infinite pyramid hotel the first guest will always leave a light on for you. ;=)
> I think I got it:
>
> https://i.ibb.co/Yj8hMmP/image.png
>
> I don't think there are any copy-and-paste error shit. ;^)
It does happen but not that often.

On Thursday, August 17, 2023 at 4:42:49 PM UTC-4, Dan joyce wrote:
> Hilbert original idea of an infinite hotel was manipulated by the
> infinite cardinals and set guys including Hilbert.(ZFC)
> His original thought of moving guest 1 to room 2 and beyond
> for the first 10 guest and then --->oo did not fit the bill
> for infinite set theory.
> rm# guest#
> ... ...
> 10 1
> 9 2
> 8 3
> 7 4
> 6 5
> 5 6
> 4 7
> 3 8
> 2 9
> 1 10
>
> That did not fit into the scheme of infinite sets.
> So they manipulated the idea using sets of guest coming into
> the hotel and also pairing the rooms off with that idea.
> My idea of an --->oo pyramid hotel is based on Hilbert's
> original idea in building the room structure bottom up
> forming a pyramid hotel. Moving each guest up one room to
> accommodated the new incoming guest. Each new line drawn is
> guest #1 turning the light on in that room and all newer guest
> behind him just move into a lighted room. Guest # 1 will never enter
> a lighted room. Keeping with the idea of never retracing a line.
> The infinite set guys did come up with a pyramid type hotel to
> fit into their scheme but pairing the rooms top down. My pyramid
> hotel is just the reverse building rooms outward and bottom up.
> Where -x --->oo and x --->oo and y --->oo
> Their manipulated version of a pyramid hotel is below.
>
> From Wikipedia
> This pairing function can be demonstrated visually by
> structuring the hotel as a one-room-deep, infinitely
> tall pyramid. The pyramid's topmost row is a single room
> : room 1; its second row is rooms 2 and 3;and so on.
>
> Where my pyramid hotel, also 1 room deep, starts at the bottom of
> the pyramid where room 1 is x=0 and is built outward in both
> directions -x\+x and upward +y forming a continuous 180 degree
> pyramid --->oo. Each line representing a room that guest #1 turns on.
> In my pyramid there can be no pairing but will --->oo in all 180
> degrees which I believe is the limit even for set theory.
>
> Just my thoughts about infinite sets and cardinals are not possible
> with this pyramid below.
> Any example that would work for ZFC is welcome.
>
> Here is the data for the pyramid again so observing this in real
> time is helpful in getting my thoughts across.
>
> Run using Chris's algorithm and set size @ 0.05 and time 50
>
> http://fractallife247.com/test/cmd_plot/
>
> RULDLURULDLDRDLULURURURDRDRDLDRURULULULULDLDLDLDRDLULURURURURURDRDRDRDRDLDRURULULULULULULDLDLDLDLDLDRDLULURURURURURURURDRDRDRDRDRDRDLDRURULULULULULULULULDLDLDLDLDLDLDLDRDLULURURURURURURURURURDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULU LULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRD RDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULU
>
> Here @ Dan's infinite pyramid hotel the first guest will always leave a light on for you. ;=)

Set Theory: Should you believe? An interesting take on the validity of infinite sets.
https://web.maths.unsw.edu.au/
Applying my --->oo pyramid hotel to ZFC where infinite cardinals are the norm, where or what would my pyramid become? I believe always --->oo.
Where does that leave ZFC?

On Friday, September 8, 2023 at 6:56:24 PM UTC-4, Dan joyce wrote:
> On Thursday, August 17, 2023 at 4:42:49 PM UTC-4, Dan joyce wrote:
> > Hilbert original idea of an infinite hotel was manipulated by the
> > infinite cardinals and set guys including Hilbert.(ZFC)
> > His original thought of moving guest 1 to room 2 and beyond
> > for the first 10 guest and then --->oo did not fit the bill
> > for infinite set theory.
> > rm# guest#
> > ... ...
> > 10 1
> > 9 2
> > 8 3
> > 7 4
> > 6 5
> > 5 6
> > 4 7
> > 3 8
> > 2 9
> > 1 10
> >
> > That did not fit into the scheme of infinite sets.
> > So they manipulated the idea using sets of guest coming into
> > the hotel and also pairing the rooms off with that idea.
> > My idea of an --->oo pyramid hotel is based on Hilbert's
> > original idea in building the room structure bottom up
> > forming a pyramid hotel. Moving each guest up one room to
> > accommodated the new incoming guest. Each new line drawn is
> > guest #1 turning the light on in that room and all newer guest
> > behind him just move into a lighted room. Guest # 1 will never enter
> > a lighted room. Keeping with the idea of never retracing a line.
> > The infinite set guys did come up with a pyramid type hotel to
> > fit into their scheme but pairing the rooms top down. My pyramid
> > hotel is just the reverse building rooms outward and bottom up.
> > Where -x --->oo and x --->oo and y --->oo
> > Their manipulated version of a pyramid hotel is below.
> >
> > From Wikipedia
> > This pairing function can be demonstrated visually by
> > structuring the hotel as a one-room-deep, infinitely
> > tall pyramid. The pyramid's topmost row is a single room
> > : room 1; its second row is rooms 2 and 3;and so on.
> >
> > Where my pyramid hotel, also 1 room deep, starts at the bottom of
> > the pyramid where room 1 is x=0 and is built outward in both
> > directions -x\+x and upward +y forming a continuous 180 degree
> > pyramid --->oo. Each line representing a room that guest #1 turns on.
> > In my pyramid there can be no pairing but will --->oo in all 180
> > degrees which I believe is the limit even for set theory.
> >
> > Just my thoughts about infinite sets and cardinals are not possible
> > with this pyramid below.
> > Any example that would work for ZFC is welcome.
> >
> > Here is the data for the pyramid again so observing this in real
> > time is helpful in getting my thoughts across.
> >
> > Run using Chris's algorithm and set size @ 0.05 and time 50
> >
> > http://fractallife247.com/test/cmd_plot/
> >
> > RULDLURULDLDRDLULURURURDRDRDLDRURULULULULDLDLDLDRDLULURURURURURDRDRDRDRDLDRURULULULULULULDLDLDLDLDLDRDLULURURURURURURURDRDRDRDRDRDRDLDRURULULULULULULULULDLDLDLDLDLDLDLDRDLULURURURURURURURURURDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULU LULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRD RDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDRDLULURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDRDLDRURULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULULU
> >
> > Here @ Dan's infinite pyramid hotel the first guest will always leave a light on for you. ;=)
> Set Theory: Should you believe? An interesting take on the validity of infinite sets.
> https://web.maths.unsw.edu.au/
> Applying my --->oo pyramid hotel to ZFC where infinite cardinals are the norm, where or what would my pyramid become? I believe always --->oo.
> Where does that leave ZFC?
Wrong web page. Use--- Set Theory: Should you believe. In a search