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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]
The Babylonians also possessed a place-value system and used a sexagesimal numeral system which is still in use today for measuring angles and time. [76] In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as the Pythagoreans appeared to have considered it a subject in its own right. [77]
As a non-positional numeral system, Roman numerals have no "place-keeping" zeros. Furthermore, the system as used by the Romans lacked a numeral for the number zero itself (that is, what remains after 1 is subtracted from 1). The word nulla (the Latin word meaning "none") was used to represent 0, although the earliest attested instances are ...
With nearly 1.4 billion people as of 2021, it accounts for about 18% of the world's human population. Africa's population is the youngest among all the continents; [10] [11] the median age in 2012 was 19.7, when the worldwide median age was 30.4. [12] Based on 2024 projections, Africa's population will reach 3.8 billion people by 2099. [13]
Tales of a Fourth Grade Nothing is a children's novel written by American author Judy Blume and published in 1972. [1] It is the first in the Fudge series and was followed by Otherwise Known as Sheila the Great , Superfudge , Fudge-a-Mania , and Double Fudge (2002).
Ethiopia, [c] officially the Federal Democratic Republic of Ethiopia, is a landlocked country located in the Horn of Africa region of East Africa.It shares borders with Eritrea to the north, Djibouti to the northeast, Somalia to the east, Kenya to the south, South Sudan to the west, and Sudan to the northwest.
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