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Psihologiadezvoltariiumaneanamunteanpdf21.ABP based smart grid systems exist and are becoming more prevalent in our everyday lives. One of the biggest challenges for consumers is inefficiency and the inability to effectively control their own consumption.
For example, electrical rates are typically adjusted for peak-times when electricity demand is at its peak, but not necessarily during times of low energy demand. The amount of electricity used by an end consumer may fluctuate dramatically. Some end consumers may decrease their electrical power consumption at times of peak demand, and may increase their consumption at times of lower demand. Controlling the consumption can be challenging for end consumers and business owners, and electric utilities have no way of tracking the amount and duration of energy consumed by the consumers.Q:

Unique function that tells when is the set strictly larger than one.

I’m wondering if there’s an algorithm that can tell when is the set $B=\{1,2,3,\ldots \}$ strictly larger than one $B>1$.
If we add $\epsilon>0$ to $1$ of its natural numbers, the set is strictly larger.
If we delete $\epsilon$ of its natural numbers the set is strictly smaller.
The algorithm must be efficient, and no unnecessary information (like sort, binary search, exponentiation, and logarithm) should be used.
PS: I have a question similar to this question, but, since I’m only looking for an algorithm for $B$ instead of $\mathbb{N}$, my problem is a bit simpler.

A:

I don’t think there’s any sort of algorithm that can do this; the problem is undecidable.
In general, the problem of testing whether a natural number is expressible as a sum of at most $n$ other natural numbers is undecidable, even in the presence of unrestricted use of the standard arithmetic operations. The proof follows from

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