Cont: Deeper than primes - Continuation 2

[jsfisher]

..deleted..


I'll wait until after you stop editing your post.

 

[doronshadmi]

..deleted..


I'll wait until after you stop editing your post.

Done.

 

[doronshadmi]

Again jsfisher, since you are fond of finitely many logical functions, then please write down all the logical functions of the 3-valued bounded logical tree (there are only 7,625,597,484,987 functions as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=11375190&postcount=1963, so it is an easy task for you).

 

[jsfisher]

Again jsfisher, since you are fond of finitely many logical functions, then please write down all the logical functions of the 3-valued bounded logical tree (there are only 7,625,597,484,987 functions as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=11375190&postcount=1963, so it is an easy task for you).

Why on Earth would I honor such a ridiculous request?

 

[jsfisher]

Well, isn't that interesting.

I made two statements, (1) that 0.01 and 0.01000000 when interpreted as paths from the root of your binary tree were different and (2) that 0.01₂ and 0.01000000₂ as base-2 values represented the same number.

Which of those two were wrong?

Both.

Well, ok, then.

0.01₂ happens to be 0.25 in the more common base-10.
0.01000000₂ also happens to be 0.25 in base-10.

...but according to Doronshadmi, the two are not the same number.

Doronshadmi has yet again demonstrated why his version of math is distinct from real Mathematics. The number 0.25 does not equal 0.25 for some values of 0.25.

 

[doronshadmi]

Why on Earth would I honor such a ridiculous request?

More finitely many logical functions more fun, jsfisher, or maybe I am wrong in case that you are fond of exactly 16 logical functions.

 

[jsfisher]

More finitely many logical functions more fun, jsfisher, or maybe I am wrong in case that you are fond of exactly 16 logical functions.

There are considerably more than 16 logical functions. And these things are a matter of fact, not fondness.

 

[doronshadmi]

0.01₂ happens to be 0.25 in the more common base-10.
0.01000000₂ also happens to be 0.25 in base-10.

If structure is also considered in case of numbers, then 0.01₂ and 0.25₁₀ do not have the same structure (they are structurally different) as clearly seen in

Now please reply to http://www.internationalskeptics.com/forums/showpost.php?p=11398220&postcount=2060.

 

[doronshadmi]

jsfisher, please also reply to http://www.internationalskeptics.com/forums/showpost.php?p=11398093&postcount=2055.

 

[jsfisher]

If structure is also considered in case of numbers, then 0.01₂ and 0.25₁₀ do not have the same structure (they are structurally different)

Numbers don't have structure. They have values. The rest is just your confused invention. It is yet another convincing example of why your math is so obviously distinct from real Mathematics.

 

[doronshadmi]

Numbers don't have structure. They have values. The rest is just your confused invention. It is yet another convincing example of why your math is so obviously distinct from real Mathematics.

Your evasion has been noted.

Only a fool would use the tree to conclude that 0.01₂ and 0.01000000₂ were different numbers.

(http://www.internationalskeptics.com/forums/showpost.php?p=11397079&postcount=2051)

Only a fool does not understand how numbers are logically directly defined along an unbounded logical tree (the needed details are already given in http://www.internationalskeptics.com/forums/showpost.php?p=11397847&postcount=2053(some typo correction: instead of "emerge form 0.01₂" it has to be "emerge from 0.01₂") and http://www.internationalskeptics.com/forums/showpost.php?p=11398093&postcount=2055).

Numbers don't have structure.

In your framework, so?

 

[jsfisher]

Your evasion has been noted.

I evaded nothing. Numbers don't have structure.

Only a fool does not understand how numbers are logically directly defined along an unbounded logical tree

You have presented nothing to relate a path in your binary trees to a numerical value, so any failure to understand that which is "logically directly defined" stems from your failure.

You have also asserted that the path represented by 0.01 down one of your binary trees (down left, then left, then right) is identical to the path represented by 0.010000 (down left, then left, then right, then down left four more times).

Everyone else understands these two paths to be different, so we anxiously await your explanation how they could possible be the same. The two paths stop at different nodes in the tree, and that right there should be enough for them to be different, but clearly you think otherwise.

 

[doronshadmi]

I evaded nothing. Numbers don't have structure.

In your framework.

You have presented nothing to relate a path in your binary trees to a numerical value,

Your evasion has been noted.

You have also asserted that the path represented by 0.01 down one of your binary trees (down left, then left, then right) is identical to the path represented by 0.010000 (down left, then left, then right, then down left four more times).

0.010000 is a bounded case of the x000... unbounded path exactly as 0.01 is a bounded case of x000... unbounded path.

Once again, in both cases Standard Math uses a default rule that determines x000... as the unbounded path of any bounded path along any unbounded logical tree (including the 2-valued unbounded logical tree).

Without this default rule 0.01₂ or 0.01000₂ are actually indeterminate since there are always infinitely many possible unbounded paths that emerge from 0.01₂ or 0.01000₂

Standard Math default rule does not work in case of 0.111... or in other words (in case of the 2-valued unbounded logical tree)
0.111...₂ ≠ 1.000...₂ , 0.0111...₂ ≠ 0.1000...₂ etc.

The following 2-valued unbounded logical tree directly logically proves that Standard Math default rule does not work along the unbounded paths among numbers like 0.111...₂ , 0.0111...₂ etc. (without loss of generality):

Unity
|\
| \
|  \
|   \
|    \
|     \
|      \
|       \
|        \
|         \
|          \
|           \
|            \
|             \
|              \
0---------------1---------------Integers
|\              |\
| \             | \
|  \            |  \
|   \           |   \
|    \          |    \
|     \         |     \         Fractions
|      \        |      \
0       1       0       1
|\      |\      |\      |\
| \     | \     | \     | \
|  \    |  \    |  \    |  \
0   1   0   1   0   1   0   1
|\  |\  |\  |\  |\  |\  |\  |\
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

              ...

In other words, you don't understand even Standard Math, in this case.

The two paths stop at different nodes in the tree, and that right there should be enough for them to be different, but clearly you think otherwise.

It does not matter, since given any bounded path along the unbounded tree, Standard Math default rule is used.

As for the radix point, your misunderstanding of it is clearly exposed in http://www.internationalskeptics.com/forums/showpost.php?p=11398093&postcount=2055 (the example there is without loss of generality).

... we anxiously await ...

Unnecessary drama.

 

[jsfisher]

I evaded nothing. Numbers don't have structure.

In your framework.

Yes, that would be Mathematics. So, we agree then; Mathematics doesn't behave the way you imagine.

You have presented nothing to relate a path in your binary trees to a numerical value,

Your evasion has been noted.

I cannot evade something you haven't presented.

You have also asserted that the path represented by 0.01 down one of your binary trees (down left, then left, then right) is identical to the path represented by 0.010000 (down left, then left, then right, then down left four more times).

0.010000 is a bounded case of the x000... unbounded path exactly as 0.01 is a bounded case of x000... unbounded path.

Ignoring your terminology invention, whether 0.01 and 0.010000 are part of other, longer paths doesn't in any way change that fact 0.01 and 0.010000 describe paths that are different from each other.


Real Mathematics doesn't work as you would fantasize it should. Sorry. It's stubborn that way.

 

[doronshadmi]

longer paths doesn't in any way change that fact 0.01 and 0.010000 describe paths that are different from each other.

Without this default rule (that determines x000... as the unbounded path of any bounded path along any unbounded logical tree (including the 2-valued unbounded logical tree)) 0.01₂ or 0.01000₂ are actually indeterminate (can't be used as distinguished numbers by Standard Mathematics) since there are always infinitely many possible unbounded paths that emerge from 0.01₂ or 0.01000₂

Real Mathematics doesn't work as you would fantasize it should. Sorry. It's stubborn that way.

jshisher, you do not understand your own reasoning, in this case.

Only a fool claims that 0.01₂ or 0.01000₂ are determinate numbers without Standard Mathematics default rule along an unbounded logical tree.

 

[jsfisher]

longer paths doesn't in any way change that fact 0.01 and 0.010000 describe paths that are different from each other.

Without this default rule (that determines x000... as the unbounded path of any bounded path along any unbounded logical tree (including the 2-valued unbounded logical tree))

The "default rule"? A bit of non-Mathematics you'd like to wedge in?

0.01₂ or 0.01000₂ are actually indeterminate (can't be used as distinguished numbers by Standard Mathenmatics)

Really? In real Mathematics, they both are representations for the same value, 0.25, a very deterministic result.

since there are always infinitely many possible unbounded paths that emerge from 0.01₂ or 0.01000₂

The sequence 0.01 and 0.010000 are representations for paths. Adding that subscript-2 would make them representations for numbers in base-2. As for the paths, though, there is no requirement either path be continued nor does any thing that might "emerge" from them change the fact they are different from each other...at least not in real Mathematics.

--------------------------
Some current Notions of Doron:

• 0.01₂ and 0.010000₂ represent different numbers (even though they both are a representation of 0.25).
• The path down a binary tree of left-left-right and the path left-left-right-left-left-left-left are exactly the same path.
• Neither 0.01₂ nor 0.010000₂ are valid numbers because they are indeterminant.

 

[doronshadmi]

Only a fool would use the tree to conclude that 0.01₂ and 0.01000000₂ were different numbers.

Only a fool claims that 0.01₂ or 0.01000₂ are determinate numbers without Standard Mathematics default rule along an unbounded logical tree.

More details are already given in http://www.internationalskeptics.com/forums/showpost.php?p=11399282&postcount=2075.

 

[doronshadmi]

--------------------------
Some current Notions of Doron:

• 0.01₂ and 0.010000₂ represent different numbers .

I do not claim such nonsense.

What I really claim about the issue at hand (logically define determinate numbers along an unbounded logical tree) is very simply addressed in http://www.internationalskeptics.com/forums/showpost.php?p=11399282&postcount=2075.

Further details are given in http://www.internationalskeptics.com/forums/showpost.php?p=11399040&postcount=2073 and http://www.internationalskeptics.com/forums/showpost.php?p=11398093&postcount=2055.

 

[doronshadmi]

Adding that subscript-2 would make them representations for numbers in base-2.

Wrong jsfisher.

It simply defines the issue at hand in terms of 2-valued unbounded logical tree.

You indeed have no clue of what is actually addressed in http://www.internationalskeptics.com/forums/showpost.php?p=11399335&postcount=2078.

 

[jsfisher]

Enjoy your made-up world. Meanwhile, Mathematics continues to work.



--------------------------
Some current Notions of Doron:

• 0.01₂ and 0.010000₂ represent different numbers (even though they both are a representation of 0.25).
• The path down a binary tree of left-left-right and the path left-left-right-left-left-left-left are exactly the same path.
• Neither 0.01₂ nor 0.010000₂ are valid numbers because they are indeterminant.