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The author gives a proof in a simple enough case that the computations are reasonable, and then indicates that "in general" the proof is similar. index battle For proofs involving objects with multiple indices which can be solved by going to the bottom (if anyone wishes to take up the effort). Similar to diagram chasing. morally true
Excessive preoccupation with indebtedness can lead to both "emotional indebtedness" and "self-debting." "Self-debting" is the inability to identify or fulfill personal needs because of such preoccupations, whereas emotional indebtedness is the accompanying stress, anxiety, feelings of hopelessness or despair, and even suicidal ideation. "Self ...
Debt is an obligation that requires one party, the debtor, to pay money borrowed or otherwise withheld from another party, the creditor.Debt may be owed by a sovereign state or country, local government, company, or an individual.
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.
Is a complex number that can be written as a real number multiplied by the imaginary unit i, [note 2] which is defined by its property i 2 = −1. [54] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. Zero is considered to be both real and imaginary. [55] implicit function
The English language has a number of words that denote specific or approximate quantities that are themselves not numbers. [1] Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles ...
This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. [ 21 ] [ 22 ] The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane ( plane geometry ) and the three ...
Azuma's inequality; Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount