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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]
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The notion of pullback as a fiber-product ultimately leads to the very general idea of a categorical pullback, but it has important special cases: inverse image (and pullback) sheaves in algebraic geometry, and pullback bundles in algebraic topology and differential geometry. See also: Pullback (category theory) Fibred category; Inverse image sheaf
Word problem (mathematics education), a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations; Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science; Word problem for groups, the problem of recognizing the identity element ...
(In the language of sheaves, pullback defines a morphism from the sheaf of smooth functions on to the direct image by of the sheaf of smooth functions on .) More generally, if f : N → A {\displaystyle f:N\to A} is a smooth map from N {\displaystyle N} to any other manifold A {\displaystyle A} , then ( ϕ ∗ f ) ( x ) = f ( ϕ ( x ...
Fix problems with image challenges when sending mail If you see an image challenge question when sending mail, you should just be able to complete the challenge then send mail. If, however, you correctly answer the image challenge and still can't send mail, it could be a sign of a more serious issue with your account, which may require ...
Most problems with viewing image attachments in AOL Mail can be fixed with a bit of trouble shooting. Try again later. If you've tried everything else and you're still not seeing images, it may be best to try again later. The problem could be caused by server delays due to a lot of people accessing their email at once.
A device that makes permanent human readable images and text from computer data. process control The field of study of automatic control of processes. programmable logic controller A computer system designed to be rugged enough for industrial use and with a programming environment highly tuned to the domain of industrial control problems.