Discussion:
rewrite: reals
Simon Roberts
2017-06-11 16:20:35 UTC
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I believe or think this expression (R) can represent any real number.

R = lim_(y->oo)

[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+

z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+

z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].

or y sufficiently large.

I believe or think this expression can represent any real number.

z_i is either 0 or 1.

x_k is any real base, including integers.

y is an integer (an index).

for example can be represented like binary.

(...1010001.011111...)_x_k

Simon Roberts.
Simon Roberts
2017-06-11 16:40:32 UTC
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Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
positive reals.
Simon Roberts
2017-06-11 17:29:52 UTC
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Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
forget this (above) lousy.

I still contend (pi)_(base 10) (1)_(base pi).

Simon.
Simon Roberts
2017-06-11 17:51:30 UTC
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Post by Simon Roberts
Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
forget this (above) lousy.
I still contend (pi)_(base 10) (1)_(base pi).
I still contend (pi)_(base 10) = (1)_(base pi).
Post by Simon Roberts
Simon.
Peter Percival
2017-06-11 18:33:32 UTC
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Post by Simon Roberts
I still contend (pi)_(base 10) = (1)_(base pi).
Try it, or try the first few digits at least.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Markus Klyver
2017-06-15 12:15:42 UTC
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Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
Sure, but you will have to choose your x_k very carefully. For example, with x_k = 0 you would only be able to represent 0.
Simon Roberts
2017-06-15 12:19:38 UTC
Raw Message
Post by Markus Klyver
Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
Sure, but you will have to choose your x_k very carefully. For example, with x_k = 0 you would only be able to represent 0.
Not sure, dude. See how I already shot down this post, idiot, go away.
Simon Roberts
2017-06-15 12:22:52 UTC
Raw Message
Post by Simon Roberts
Post by Markus Klyver
Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
Sure, but you will have to choose your x_k very carefully. For example, with x_k = 0 you would only be able to represent 0.
Not sure, dude. See how I already shot down this post, idiot, go away.
I know greater than 1 and less than or equal to two will work. Agree, idiot? Why don't you state your choice for x_k instead being patronising, goof. How old are you, anyway.
Markus Klyver
2017-06-15 13:04:54 UTC
Raw Message
Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
Also, your claim is trivially true. Say we want to represent some real number a. Let x_k = a. Then let z_1 = 1 and z_k = 0 for all k ≠ 1.
Simon Roberts
2017-06-15 13:53:16 UTC
Raw Message
Post by Markus Klyver
Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
Also, your claim is trivially true. Say we want to represent some real number a. Let x_k = a. Then let z_1 = 1 and z_k = 0 for all k ≠ 1.
Let's say we don't want.
Markus Klyver
2017-06-15 14:20:24 UTC
Raw Message
Post by Simon Roberts
Post by Markus Klyver
Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
Also, your claim is trivially true. Say we want to represent some real number a. Let x_k = a. Then let z_1 = 1 and z_k = 0 for all k ≠ 1.
Let's say we don't want.
Don't want what?
Simon Roberts
2017-06-15 22:15:25 UTC
Raw Message
Post by Markus Klyver
Post by Simon Roberts
Post by Markus Klyver
Post by Simon Roberts
I believe or think this expression (R) can represent any real number.
R = lim_(y->oo)
[(z_(-y)(x_k)^(-y) + z_(-y+1)(x_k)^(-y+1) + z_(-y+2)(x_k)^(-y+2) +...+
z_(-1)^(-1) + z_(0)(x_k)^(0) + z_(1)(x_k)^(1) +...+
z_(y-2)(x_k)^(y-2) + z_(y-1)(x_k)^(y-1) + z_(y)(x_k)^(y)].
or y sufficiently large.
I believe or think this expression can represent any real number.
z_i is either 0 or 1.
x_k is any real base, including integers.
y is an integer (an index).
for example can be represented like binary.
(...1010001.011111...)_x_k
Simon Roberts.
Also, your claim is trivially true. Say we want to represent some real number a. Let x_k = a. Then let z_1 = 1 and z_k = 0 for all k ≠ 1.
Let's say we don't want.
Don't want what?
twit.
Simon Roberts
2017-06-21 02:52:00 UTC
Raw Message
found it.

Mathematics:
Axiom: k is any of 0,1,2,3,...,n.
Axiom: There are no "negative" "quantities".
Axiom: There are no "infinite" "quantities".
Axiom: "quantities" are "unlimited".
A sufficient expression for any and all "quantities":
x_(-k)*y^(-k) + x_(1-k)*y^(1-k) + ...
+ x(-1)y^(-1) + x_0 + x_(1)y^(1) +
... + x_(k-1)y^(k-1) + x_(k)*y^(k),
where y is two and x_i either is 0 or is 1.
Then everything else an application of LOGIC and logical concepts.
Such as,
"minus" and
i^2 = -1.
Simon C . Roberts
Markus Klyver
2017-06-27 01:49:31 UTC
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Is this meant as an construction of the reals?
Simon Roberts
2017-06-27 03:27:30 UTC
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Post by Markus Klyver
Is this meant as an construction of the reals?
It is.
Markus Klyver
2017-06-27 10:23:56 UTC
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My only problem with this is that you seem to assume the existence of reals in your construction. You can't have irrational limits of you don't already have reals.
Simon Roberts
2017-06-27 10:47:37 UTC
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Post by Markus Klyver
My only problem with this is that you seem to assume the existence of reals in your construction. You can't have irrational limits of you don't already have reals.
do you have a problem that reals exist? (trick question).

Markus, they could be for example bits including bits less than one, and an unlimited amount. I'm not a big believer in infinity when, say, trying to describe or write an irrational number in binary say. The universe would become a singularity before this could ever be done. Try representing Pi for example in binary, yes the entire number, whether it exists or not, ok?
Markus Klyver
2017-07-06 19:48:45 UTC