The Universe of Discourse

A message to the aliens, part 2/23 (arithmetic)

Earlier articles: Introduction Common features Page 1 (numerals)

This is page 2 of the Cosmic Call message. An explanation follows.

Reminder: the previous page explained the ten digits:

0

1

2

3

4

5

6

7

8

9

This page, headed with the glyph for “mathematics” , explains the arithmetic operations on numbers.

The page is in five sections, three on top and two below.
The first four sections explain addition , subtraction , multiplication , and division . Each is explained with a series of five typical arithmetic equalities. For example, !!4\times 3= 12!!:

The subtraction sign actually appeared back on page 1 in the Mersenne prime !!2^{3021377}-1!! .

The negative sign is introduced in connection with subtraction, since !!1-2={}^-1!!:

Note that the negative-number sign is not the same as the subtraction sign.

The decimal point is introduced in connection with division. For example, !!3\div 2 = 1.5!!:

There is also an attempt to divide by zero:

It's not clear what the authors mean by this; the mysterious glyph does not appear anywhere else in the document. What did they think it meant? Infinity? Indeterminate? Well, I found out later they published a cheat sheet, which assigns the meaning “undetermined” to this glyph. Not a great choice, in my opinion, because !!1÷0!! is not numerically equal to anything.

For some reason, perhaps because of space limitations, the authors have stuck the equation !!0-1 = {}^-1!! at the bottom of the division section.

The fifth section, at lower right, displays some nonterminating decimal fractions and introduces the ellipsis or ‘…’ symbol. For example, !!1\div 9 = 0.1111\ldots!!:

I would have put !!2÷27 = 0.0740…!! here instead of !!2\div 3!!, which I think is too similar to the other examples.

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