Discussion:
rewrite: reals
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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).

Sorry about that.

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
Sorry about that.
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
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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
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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
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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.
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
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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
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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
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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
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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

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