## Subtraction terms

Contents

Mathematics is a scientific discipline that is often difficult to understand due to its complexity and abstract dimension. However, the basic arithmetic operations are known to the vast majority of the population.

Multiplication is a form of addition but in an abbreviated form. The characteristic sign of this operation is x. Thus, 3×4 is the same as saying 3+3+3+3+3. To exercise this type of operations most schoolchildren around the world become familiar with the famous multiplication tables.

Anthropologists consider that the numerical ability of early homo sapiens was very rudimentary, but effective enough to understand basic ideas related to addition and subtraction of things.

### Subtractions with result

This is a sum of a sequence, whose nth term is the sum of the first n terms of the infinite series; that is, all the elements of an infinite set are added; however, in reality the limit of all the elements that are added is calculated and the mathematical limit is calculated.

The summands are placed in successive rows by arranging the numbers in columns, starting on the right with the number of units (U), on the left with the tens (D), the next with the hundreds (C), the next with the thousands (M), and so on.

Normally the carries are not noted on the paper, adding directly the carry to the summands of the following column and the aspect of the realization of the sum without the auxiliary annotations would be the following:

### Addition, subtraction, multiplication and division as they are called

The + (addition) and – (subtraction) signs. The first time the signs + (plus) and – (minus) appear in a printed book, as far as is known today, is in the work Mercantile Arithmetic, or Behende und hubsche Rechenung au allen Kau manscha, by the German mathematician Johannes Widman (1462 – 1498), published in Leipzig in 1489. However, Widman does not use the signs + and – as symbols of the arithmetical operations addition and subtraction, but, within the commercial practices analyzed in the text, to express excess and defect of goods, for example, in the weight of barrels. In the following image we see “4 + 5” which means “4 centner + 5 pfund” or “5 – 17” expressing “5 centner – 17 pfund”, where we remember that the “centner” and the “pfund” are German units of weight, that 1 “centner” is 100 “pfund”, and one “centner” is equivalent to 50 kilograms.

The arithmetic book of the Dutch mathematician Van der Hoeke (16th century) is often cited as the first printed publication in which the signs + and – appear as algebraic operations, as it is usually dated its publication in 1514, however, this is from 1937 (the date 1514 is an error related to the 1944 edition). As Florian Cajori mentions, the first printed publication with the algebraic meaning of these signs is the algebra and arithmetic book Ayn new Kunstlich Beuch (1518), by the German mathematician Henricus Grammateus (ca. 1492-1525).

### What is subtraction

You may not be very familiar with the concept of neutral element or identity element on the one hand, and that of symmetric element on the other. Both are defined for a given operation (we are going to present them for addition, in this case).

Simply put, the neutral element or identity element of the sum of functions is the one that when operated with any other element, in this case any other function, gives as a result the function itself. As you can see, it is the element that has a neutral effect when applied with any other element the operation for which it is defined.

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