Friday, February 24, 2006

1 = 0.999999999…

1 = 0.999999999…

An oriental girl at last won the Olympic Games’ Gold Medal in figure skating competition, as a report from Turin or Torino told. She happens to be Japanese, which however does not necessarily mean she is No.1 or the best among skating girls in Japan.

Figure is really an interesting term. By mastering geometry, ancient Greeks laid the foundation for future European civilization which has been realized and boosted by Christianity. It is taught as collaboration of Hellenism and Hebraism in Japan just like in other civilized regions.

Japan had, in old days, no tradition of stone architecture comparable to Europe, for there have been plenty of woods and a wealthy of other products of nature. Geometry had not a great chance to develop in Japan. But, it has not hindered the development of scientific talent and the love for science among the race.

In terms of the very basic thing, some educated Japanese are for example still arguing how to explain the following equation in earnest.

1 = 0.9999999999999999999999999999999999999999999…

According to modern mathematics, there is no such a number as is less than “one” but larger than any other number that is also less than “one.”

However, there is a number that is equal to, or less than, “one” and larger than any other number that is less than “one.” This number is “one” itself.

(Correctly. 1 is a number that is larger than any other number that is less than 1.)

The number in the infinite expression in the right side of the equation means the number which is larger than any other number that is less than one.

Therefore, the above equation is correct.

There is no secret or mystery in the infinite series of the number 9. The equation itself is an indicative one, which emphasizes neither the format nor the arithmetic operation implied therein but the meaning assumed for the expression with infinitesimals.

To my surprise, there are some Japanese still arguing how to explain the above equation. But, mostly the discussions are not accompanied by religious atmosphere even though philosophical sometimes.

Olympic Games must be a religious event originally to show human, clean bouts to Greek Gods. Then figure skating must have a religious meaning, too. But, it looks very fleshly nowadays.

When human beings understand the nature of numbers one-step deeper, God might be rejoiced. And, when skating girls perform well one more rotation in air on a certain figure, God might be also rejoiced.

But, God would be surely more satisfied to see peace in Baghdad and other cities of conflict nowadays.

Mathematics is said to be Queen of Science. And the number theory is said to be Queen of Mathematics, but geometry is not.

The number theory has its origin in ancient Mesopotamia. Someday, their descendants, including modern Iraqis and Jews, might win a gold medal again in human history.

1/3 = 0.33333333....
2/3 = 0.66666666...
1 = 1/3 + 2/3 = 0.99999999....)