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In arithmetic, and therefore algebra, division by zero is undefined. [7] Use of a division by zero in an arithmetical calculation or proof, can produce absurd or meaningless results. Assuming that division by zero exists, can produce inconsistent logical results, such as the following fallacious "proof" that one is equal to two [ 8 ] :
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Some authors of abstract algebra textbooks define an indeterminate over a ring R as an element of a larger ring that is transcendental over R. [3] [4] [5] This uncommon definition implies that every transcendental number and every nonconstant polynomial must be considered as indeterminates.
An underdetermined linear system has either no solution or infinitely many solutions. For example, + + = + + = is an underdetermined system without any solution; any system of equations having no solution is said to be inconsistent.
WASHINGTON (Reuters) -U.S. officials are communicating with people in Syria to seek information about Austin Tice, an American journalist captured there more than 12 years ago, White House ...
While that 215,000 figure in 2026 is only 5.3% of all vehicles coming off leases in the US, it will be significantly higher than the approximate 1.5% projected for 2024 and 2025.
A partial function arises from the consideration of maps between two sets X and Y that may not be defined on the entire set X.A common example is the square root operation on the real numbers : because negative real numbers do not have real square roots, the operation can be viewed as a partial function from to .
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