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Traden4Alpha
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Re: True or false

November 1st, 2016, 3:00 pm

Yes, "unique factorisation" is a nice argument yet it seems to say more about the human mind (which finds uniqueness to be elegant or at least easier to think about) than it does math (which has no qualms about infinite sets).

This is beginning to remind me of the arctan and inverse abs threads in which someone vehemently defended the arbitrary convention of picking a particular single value as the only "correct" solution of a multivalued mathematical relation.
 
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katastrofa
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Re: True or false

November 1st, 2016, 3:18 pm

About whose mind?
20150409_185441.jpg
 
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Traden4Alpha
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Re: True or false

November 1st, 2016, 3:24 pm

Which ever mind is more curious!
 
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outrun
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Re: True or false

November 1st, 2016, 4:22 pm

This is beginning to remind me of the arctan and inverse abs threads ...
wo! That escalated quickly!
 
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Traden4Alpha
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Re: True or false

November 1st, 2016, 5:03 pm

This is beginning to remind me of the arctan and inverse abs threads ...
wo! That escalated quickly!
LOL!

The power of math is in it's infinite optionality. As a logical system, one is free to synthesize and select axioms at will although all such axiom sets of modest power will be either incomplete or inconsistent. It's a separate issue of science whether some axiom sets are "true" in the real world and an even more interesting question for engineering whether some axiom sets are useful (which may be a disjoint set from the scientifically true set of axiom sets).

One common use of inverse "functions"* is to model which antecedent system states may have preceded a given measured consequent system state.

* NB: this is the loose definition of "function" which permits multivalued results (perhaps disguised as a single value which just happens to be a multi-element set.)
 
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outrun
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Re: True or false

November 1st, 2016, 5:30 pm

I was reading a bedtime story yesterday about Euclid's five axioms. The fifth axiom about the parallel lines confused people and for more than a 1000 years they tried to prove that it was not an axiom, but that it could be deduced from the other four. Then Gauss (and two others who's name didn't ring a bell) came alone and sorted it out, and non-Euledian geometry was born!

The inverse abs was interesting because it was an internally conflicting set of axioms, and then you can conclude *anything* as a true (or false) statement.

About multi values results: I classify them into two sets, multi valued results that can be mapped to a single value (bit strings of infinite length), and those you can't.
 
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Cuchulainn
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Re: True or false

November 2nd, 2016, 8:40 am

That would agree. Galois and the beginning of the set theory is the early 19th century and it took it over half a century to go mainstream, if I remember rightly. Since 1 is a neutral element of the real number set, it cannot be consider either prime or complex (one does not include it among prime factors as it wouldn't give a unique factorisation - you can multiply by 1 as many times are you want, and hence deny the fundamental theorem of arithmetic.
It's called idempotence

https://en.wikipedia.org/wiki/Idempoten ... d_examples

// And TChebychev's counting theorem breaks down when n = 1.
Last edited by Cuchulainn on November 2nd, 2016, 10:35 am, edited 2 times in total.
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Cuchulainn
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Re: True or false

November 2nd, 2016, 10:24 am

This is going to be the longest thread ever, Whitehead Russell needed more than a 1000 pages to prove that 1+1=2
But before we can continue where they left of we need to establish precisely what your symbol '''1'" represent? My initial reaction was that it was a python string of length 1 (no semicolon at the end of the line). Or is it a reference to a number? What type of number? Can you list the axiomas of that number system, explain the symbols you use and the operations one can use to manipulate those symbols?
Yes, Peano did it
https://en.wikipedia.org/wiki/Peano_axioms

// It will never be longer than [$]e^5[$] thread.
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Traden4Alpha
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Re: True or false

November 2nd, 2016, 10:36 am

The story of Euclid fifth is delightful in showing the arbitrariness of axioms as well as the differences between math, science, and engineer. In math, you get to pick. In science, the fifth is false (gravitational warping of space-time). And in engineering, the fifth is almost always used as true (e.g., in making CAD drawings of most manufactured objects).

To me, multivalued results are a bit like quantum superposition of states and a function like invabs() creates an output that is a superposition of both negative and positive branches. The abs() function collapses the states.

The view that a single value (e.g., the input or output to a primitive function) could be a set comes from using APL in which the operators had no problems handling set-valued arguments or in outputting set-valued results.
 
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Cuchulainn
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Re: True or false

November 2nd, 2016, 12:36 pm

The biologist says "I study the principles of life."
The psychologist says "You are controlled by the principles of life."

The businessman says "My business can use its force to control the economy."
The economist says "The forces of the economy will control your business."

The engineer says: "My equations are a model of the universe."
The physicist says: "The universe is a model of my equations."

The mathematician says: "I don't care."
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JGJPR
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Re: True or false

September 10th, 2017, 6:37 pm

This exercice is not clear. Such text must be extremely precise.

"with each power of two having an equal probability"

This does not mean anything. A number has no probability, but an event, yes. So what does it mean?

"and each possible distribution being equally likely for a certain true count"

I think this is the worst one. A "distribution equally likely", is the distribution random?! I suggest the writer to type "distribution of probability" on google and learn. Once done, what did s/he mean?

"Assuming Albert guesses optimally"

Optimality is here undefined. So, again, same question, what does it mean?
 
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outrun
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Re: True or false

September 10th, 2017, 7:07 pm

This exercice is not clear. Such text must be extremely precise.

"with each power of two having an equal probability"

This does not mean anything. A number has no probability, but an event, yes. So what does it mean?

"and each possible distribution being equally likely for a certain true count"

I think this is the worst one. A "distribution equally likely", is the distribution random?! I suggest the writer to type "distribution of probability" on google and learn. Once done, what did s/he mean?

"Assuming Albert guesses optimally"

Optimality is here undefined. So, again, same question, what does it mean?
When you "throw 6"with a dice you don't ask "six what? six times against the wall?? six months?? six different colours??" .. it's obvious that 6 is the event where the outcome is 6 eyes.
The other one sound like the prior of a Bernoulli trial conditioned on  certain nr of succeses? 
 
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outrun
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Re: True or false

September 10th, 2017, 7:15 pm

This sounds like "the furious ranting autism test", they do this deliberately and observe your reaction. They don't care about statistics, they only care about how you react is situations that are I'll posed -like in the real worlds-.

Was there a big mirror on the wall when you did this test ?
 
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Cuchulainn
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Re: True or false

September 10th, 2017, 8:27 pm

This exercice is not clear. Such text must be extremely precise.

I agree. 
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Paul
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Re: True or false

September 11th, 2017, 6:32 am

What's the FRA Test?!
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