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The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
Many word problems are undecidable based on the Post correspondence problem. Any two homomorphisms, with a common domain and a common codomain form an instance of the Post correspondence problem, which asks whether there exists a word in the domain such that () = (). Post proved that this problem is undecidable; consequently, any word problem ...
The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra. As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.
Squaring the circle, the impossible problem of constructing a square with the same area as a given circle, using only a compass and straightedge. [7] Three cups problem – Turn three cups right-side up after starting with one wrong and turning two at a time. [8]
She adds that using the word “should” can unwittingly lead to feelings of shame, as if they should have already known and done better. Dr. Danda points to one alternative: “I have some ideas ...
People didn't just fill their plates this Thanksgiving weekend -- data shows they also filled their online shopping carts. Black Friday online shopping this year set a new high, reaching $10.8 ...
The first five editions of Darwin's in Origin of Species used the word "evolved", but the word "evolution" was only used in its sixth edition in 1872. [8] By then, Herbert Spencer had developed the concept theory that organisms strive to evolve due to an internal "driving force" ( orthogenesis ) in 1862. [ 7 ]
It’s called sticker shock. And if you haven’t been to a dealer’s showroom since before the pandemic, you might want to prepare yourself.