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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 ] :
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 January 2025. Look up undefined in Wiktionary, the free dictionary. Undefined may refer to: Mathematics Undefined (mathematics), with several related meanings Indeterminate form, in calculus Computing Undefined behavior, computer code whose behavior is not specified under certain conditions Undefined ...
2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.
Despite these subtle logical problems, it is quite common to use the term definition (without apostrophes) for "definitions" of this kind, for three reasons: It provides a handy shorthand of the two-step approach. The relevant mathematical reasoning (i.e., step 2) is the same in both cases. In mathematical texts, the assertion is "up to 100%" true.
In theory, Trump could issue a blanket pardon to cover all Jan. 6 defendants who were charged or convicted of misdemeanors. VIOLENT OFFENDERS.
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For example, squares (resp. triangles) have 4 sides (resp. 3 sides); or compact (resp. Lindelöf) spaces are ones where every open cover has a finite (resp. countable) open subcover. sharp Often, a mathematical theorem will establish constraints on the behavior of some object; for example, a function will be shown to have an upper or lower bound.
Booze makers are getting an early hangover after the US surgeon general called for the addition of a warning label to alcoholic drinks. On Friday, shares of beer and alcohol giants sank across the ...