Even number

No seeing the number is difficult to guess what it is - an even number or odd. But do not think that you will always be able to say it, almost see the defined number. Parity in number theory - characteristics of a number that determines its ability to divide evenly into two. Say, for example, 16 - odd or even number? If the decimal notation of the last digit is an even number (0, 2, 4, 6 or 8), then all of it is also even, otherwise - odd.

No seeing the number is difficult to guess what it is - an even number or odd

If you know that it is written in the decimal system, then you may say that it is an even number. But when it is written on any other system - is it possible to be sure that it necessarily shows an even number?

The answer is no. If the base is, for example, seven, then 16 = 7 + 6 = 13 is odd. The same will happen to any odd base (because every odd number + 6 there is also an odd number).

Hence the conclusion that the familiar sign of divisibility by 2 (the latter figure is an even number), of course, only suitable for the decimal number system, for others - not always. That is, it is true only for the number system with an even basis: senary, octal, etc. What is the sign of divisibility by 2 for systems with an odd basis? Suffice brief reflections to install it: sum of the digits must be an even number. For example, the number 136 is an even number in any number system; indeed, in the latter case we have an odd number + an odd number + even number = even number.

An even number from ancient times often attached mystical significance. In Chinese cosmology an even number corresponds to the concept of "yin" and the odd - "yang".

For example in the US, Europe and some eastern countries it is considered that an even number of flowers brings happiness. In the CIS countries adopted an even number of flowers bring only the deceased's funeral. However, in cases where a bouquet of flowers a lot (more than 11), parity and oddness of their number does not play any role. For example, it is permissible to give the lady a bouquet of 12, 14, 16 and so on.

Tools