1) Humans have been using numbers to count with for thousands of years.
2) Romans did all their calculating on a counting board, which was an early version of an abacus.
3) There are lots of different kinds of numbers that you’ll come across in algebra, and a lot of these kinds of numbers are related to each other.
4) Numbers and counting didn’t truly come into being until the rise of cities.
5) The ancient Greek mathematician Pythagoras believed that all numbers were rational, but one of his students Hippasus proved that you could not represent the square root of 2 as a fraction, and so it was irrational.
6) Rational number is any number that can be made by dividing one integer by another.
7) The most primitive method of representing a natural number is to put a dot for each object.
8) The ancient Egyptians developed a powerful system of numerals, with distinct hieroglyphs for 1, 10 up to over 1 million.
9) A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral.
10) German mathematician Gottfried Leibnitz invented a system of counting that used only ones and zeroes; what would eventually be called the binary system.
11) In India, negative numbers did not appear until about 620 CE in the work of Brahmagupta (598 - 670) who used the ideas of 'fortunes' and 'debts' for positive and negative.
Соотнесите следующие эквиваленты с выделенными жирным курсивом словами в тексте.
Подмножества рациональных чисел, натуральные числа, отрицательные числа, целые числа (2), неправильные дроби, распространённое математическое обозначение, рациональные числа, дробь, правильные дроби, иррациональное число, знаменатель, числитель, достоинство (стоимость), пропорция.