Comment Re:Man = 1000 (Score 1) 162
It was intended as a joke, illustrating, exactly as you said, "iconiclastic pedantry".
Comment Re:Man = 1000 (Score 1) 162
Infinite places does not mean everywhere. This is a common misconception when dealing with infinite sets.
Suppose you have infinite many places, as many as the natural numbers.
You may have infinitely many places numbered by even numbers, while still not have the other, infinitely many, places with odd numbers.
So a more correct translation would be "in many places". But then again, if you are talking about infinite sets, the concept of "many" is also tricky, and leads into questions of set cardinality, aleph numbers, etc. which fortunately is a lot more interesting than the usual Netflix soap operas.
Comment Re:The proof program (Score 1) 143
#The range should not include 0 - so much for trying to be concise...
range(1,N+1)
range(1,N+1)
Comment The proof program (Score 1) 143
# Claim: It is not possible to make a partition of the
# natural numbers into to sets so that
# _all_ pythagorean tripples are split up,
# having some elements in one partition and
# some in the other.
#
# The math proof relies on this being true for all triples
# of numbers up to N = 7285, something which can be tested by
# a computer.
#
# We create a logic expression that is true iff
# there exists some partition such that all triples
# are split, and false otherwise. The computer
# checks that this is indeed always false (=unsatisfiable)
# for all possible partitions.
#
# Below P13 means that integer 13 belongs to the first set
# and ~P13 means that it belongs to the other set, etc.
from sympy import *
N = 10 # should be 7285
def is_a_triple(a,b,c): return a**2+b**2==c**2
tripplesUpToN=[(a,b,c) for a in range(N) for b in range(N) for c in range(N) if is_a_triple(a,b,c)]
def notAllInSamePartition(a,b,c):
Pa,Pb,Pc=var("P{} P{} P{}".format(a,b,c)) # Create variables P13, P57, etc.
return ~( (Pa & Pb & Pc) | (~Pa & ~Pb & ~Pc) )
# Expr = All triples of numbers up uo N are split up over different partitions
Expr = And(*[notAllInSamePartition(a,b,c) for a,b,c in tripplesUpToN])
# Expr is unsatisfiable, because always some triple will be completely in one of the partitions, so it should print False
print satisfiable(Expr)
# natural numbers into to sets so that
# _all_ pythagorean tripples are split up,
# having some elements in one partition and
# some in the other.
#
# The math proof relies on this being true for all triples
# of numbers up to N = 7285, something which can be tested by
# a computer.
#
# We create a logic expression that is true iff
# there exists some partition such that all triples
# are split, and false otherwise. The computer
# checks that this is indeed always false (=unsatisfiable)
# for all possible partitions.
#
# Below P13 means that integer 13 belongs to the first set
# and ~P13 means that it belongs to the other set, etc.
from sympy import *
N = 10 # should be 7285
def is_a_triple(a,b,c): return a**2+b**2==c**2
tripplesUpToN=[(a,b,c) for a in range(N) for b in range(N) for c in range(N) if is_a_triple(a,b,c)]
def notAllInSamePartition(a,b,c):
Pa,Pb,Pc=var("P{} P{} P{}".format(a,b,c)) # Create variables P13, P57, etc.
return ~( (Pa & Pb & Pc) | (~Pa & ~Pb & ~Pc) )
# Expr = All triples of numbers up uo N are split up over different partitions
Expr = And(*[notAllInSamePartition(a,b,c) for a,b,c in tripplesUpToN])
# Expr is unsatisfiable, because always some triple will be completely in one of the partitions, so it should print False
print satisfiable(Expr)
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