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A Taxicab number is the smallest positive number that can be expressed as a sum of two positive integer cubes in n distinct ways. The smallest taxicab number after Ta(1) = 1, is Ta(2) = 1729, [4] expressed as
[2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...
The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function : polynomial of degree zero, graph is a horizontal straight line Linear function : First degree polynomial, graph is a straight line.
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
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]
If we were to express this idea using symbols of grouping, the factors in a product. Example: 2+3×4 = 2 +(3×4)=2+12=14. In understanding expressions without symbols of grouping, it is useful to think of subtraction as addition of the opposite, and to think of division as multiplication by the reciprocal.
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