Question

define the set of natural number with examples. does 'zero' belongs to the set? what would happened if 'zero' was not invented? imagine the world without 'zero'​

Answer 1

Answer:

The set of natural numbers is an infinite set. By definition, this kind of infinity is called countable infinity. All sets that can be put into a bijective relation to the natural numbers are said to have this kind of infinity. This is also expressed by saying that the cardinal number of the set is aleph-nought (ℵ0).

Step-by-step explanation:

Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobbets. He developed a symbol for zero: a dot underneath numbers. "But he, too, does not claim to have invented zero, which presumably must have been around for some time," Gobbets added.

"We now know that it was as early as the third century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics have been in the Indian sub-continent for centuries."

From the Middle East to Wall Street

Over the next few centuries, the concept of zero caught on in China and the Middle East. According to Nils-Bentil Wallan of Yale Global, by 773, zero reached Baghdad where it became part of the Arabic number system, which is based upon the Indian system.

A Persian mathematician, Mohammed ibn-Musa al-Khwarizmi, suggested that a little circle should be used in calculations if no number appeared in the tens place. The Arabs called this circle "sifr," or "empty." Zero was crucial to al-Khwarizmi, who used it to invent algebra in the ninth century. Al-Khwarizmi also developed quick methods for multiplying and dividing numbers, which are known as algorithms — a corruption of his name.