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bio website math.ubc.ca/~israel
location Richmond, Canada
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visits member for 3 years, 1 month
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I'm an Emeritus Associate Professor of Mathematics at University of British Columbia and an Optimization Algorithms Researcher at D-Wave Systems in Burnaby BC


Apr
11
comment Reducing a Decidability Problem to the Halting Problem
$S$ is part of the specification of the problem. That is, in a particular instance, you are given a specific machine $M$ and a specific set $S$ (presumably its members are of whatever type is acceptable as inputs to $M$), and you ask whether there are fewer than $n$ members of $S$ on which $M$ halts. Note that if the answer is No (i.e. there are at least $n$ such members), you can prove that by running $M$ on $n$ different inputs and seeing that it does indeed halt in each of those cases. A Yes answer, on the other hand, might not be provable.
Apr
11
revised Is $C(X)$ dense in $L^p$?
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Apr
11
comment Is $C(X)$ dense in $L^p$?
Sorry, I meant $X = \mathbb R$.
Apr
11
answered Is $C(X)$ dense in $L^p$?
Apr
11
comment Is $C(X)$ dense in $L^p$?
That theorem is about $C_c(X)$, not $C(X)$. There are also some additional assumptions on $\mu$.
Apr
11
answered Reducing a Decidability Problem to the Halting Problem
Apr
11
comment How would go about creating the chart used in the link provided?
Is there a math question here? Are you asking for how the data were gathered, or what the numbers represent, or what software was used for producing the chart from the data? None of these questions is really appropriate for this site, I think.
Apr
11
answered How to show that $f(x)$ is never negative
Apr
11
answered Precise definition of a “game of incomplete information” (Game Theory)
Apr
11
comment word for equivalence class of vectors such that v ~ av for all non-zero scalars a
In quantum mechanics the scalars are complex, so this distinction does not occur. Another alternative is to say "one-dimensional subspace".
Apr
11
comment limiting probability - what matrix to write
Use whatever method you use to solve $A x = b$.
Apr
11
comment Concerning types of square-free numbers.
The number of which $2$-primes and $3$-primes?
Apr
11
revised Concerning types of square-free numbers.
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Apr
11
revised Concerning types of square-free numbers.
added 1022 characters in body
Apr
11
comment Concerning types of square-free numbers.
$102 = 2 \times 3 \times 17$ and $105 = 3 \times 5 \times 7$ are consecutive $3$-primes with no $2$-prime between them: $103$ is a prime and $104$ is not square-free.
Apr
11
comment Concerning types of square-free numbers.
Your list is incorrect. For example, you left out $[230,231]$.
Apr
11
answered Concerning types of square-free numbers.
Apr
10
comment Find all natural numbers $x$ such that …
Product of their digits (or more precisely, their digits in base $10$).
Apr
10
revised Which do you prefer sine or cosine?
added 87 characters in body
Apr
10
answered Which do you prefer sine or cosine?