Infinity

The term infinity corresponds to several different concepts, depending on the field of application, be it mathematics, physics, philosophy, theology or everyday life. Infinity is alien to our immediate experience, and in most cultures has emerged as an abstract quantitative designation of something inconceivable, in application to entities without spatial or temporal boundaries. Also infinity is inextricably linked with the designation of infinitesimal.

The term infinity corresponds to several different concepts, depending on the field of application, be it mathematics, physics, philosophy, theology or everyday life

You can imagine infinity if you try to count the number of grains of sand on the beach, the number of stars in the sky, etc. Nevertheless, although we can not name the exact number of grains of sand on this beach, we understand that this amount is very large, but still finite number. As for the number of visible stars in the sky (and there are also invisible stars), then, according to modern physical concepts, even the number of atoms in Universe does not exceed 10 in the tenth and once again in the tenth degree. Thus, in the real physical world, we can not detect infinity. What does this mean? What role does infinity play in mathematics? This means only that if any concept has no analogue in physical reality, then it is expedient to look at it only from the point of view of the usefulness it brings to our thinking.

Infinity prompted meditations back in antiquity. Maya used zero in your twentieth number system almost a millennium before the Indians. It is curious that the sign (0) of the Maya mathematicians also denoted infinity.

Brilliant work of Indian mathematicians was received by arab mathematicians, thanks to which she moved to conquer Europe. But, as it often happened, and here problems with infinity were resolved far from immediately. It is significant that the winner of the competition, the Swiss mathematician S. Liuillet, presented the work under the motto: "Infinity is the abyss in which our thoughts sink". And, nevertheless, infinity was not alien to European mathematicians. The fact that 1/0 is precisely the number, and not the limit of the function, is said back in the 18th century Euler!

The famous Georg Kantor was the only mathematician and philosopher who believed that infinity not only exists but is also fully understood by man, and that this comprehension will lift mathematicians, and after them theologians, all the more - closer to God. He devoted his life to this task. Cantor's persistent desire to view infinity as something topical was a great news for that time. A familiar sign indicating the infinity "∞" was introduced back in 1655 by the English mathematician John Wallis. This sign is used by every high school student when recording the domain of the function change, finding limits, etc. The sign of infinity gradually became familiar not only for mathematicians, but also found in everyday life.

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