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Cantor proved that the cardinality of the second number class is the first uncountable cardinality. [12] Cantor's second theorem becomes: If P ′ is countable, then there is a countable ordinal α such that P (α) = ∅. Its proof uses proof by contradiction. Let P ′ be countable, and assume there is no such α. This assumption produces two ...
The numbers 200-900 would be confused easily with 22 to 29 if they were used in chemistry. khīlioi = 1000, diskhīlioi = 2000, triskhīlioi = 3000, etc. 13 to 19 are formed by starting with the Greek word for the number of ones, followed by και (the Greek word for 'and'), followed by δέκα (the Greek word for 'ten').
(The rule stated above may also be remembered by the word FOIL, suggested by the first letters of the words first, outer, inner, last.) William Betz was active in the movement to reform mathematics in the United States at that time, had written many texts on elementary mathematics topics and had "devoted his life to the improvement of ...
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc., with the suffix acting as an ordinal indicator. Written dates often omit the suffix, although it is nevertheless pronounced.
First-order approximation is the term scientists use for a slightly better answer. [3] Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has 4 × 10 3, or four thousand, residents"). In the case of a first-order approximation, at least one number given is exact.
When S > L there are only 2L+1 orientations of total angular momentum possible, ranging from S+L to S-L. [2] [3] The ground state of the nitrogen atom is a 4 S state, for which 2S + 1 = 4 in a quartet state, S = 3/2 due to three unpaired electrons. For an S state, L = 0 so that J can only be 3/2 and there is only one level even though the ...
A mnemonic is a memory aid used to improve long-term memory and make the process of consolidation easier. Many chemistry aspects, rules, names of compounds, sequences of elements, their reactivity, etc., can be easily and efficiently memorized with the help of mnemonics.