Types of Numbers in Math | ASMR whisper

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Description: The first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers.

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The ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1, 10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC depicts 276 as 2 hundreds, 7 tens, and 6 ones; and similarly for the number 4,622. The Babylonians had a place-value system based essentially on the numerals for 1 and 10, using base sixty, so that the symbol for sixty was the same as the symbol for one, its value being determined from context.

There's counting numbers like these that our ancestors used, there's the more abstract "zero" that generally took longer for the Egyptians, Babylonians, Indians, Chinese, Meso-Americans, and Greeks, then came numbers in the opposite 2-dimensional direction, known as negative integers.

The next step was dividing one integer by another, called a fraction, that can also be expressed as a finite decimal. Seems rational. Then came weirdly irrational numbers that could not be expressed as a decimal with a definite end. The Egyptians and Pythagoreans knew how strange it was that a number multiplied by itself to get exactly 2, did not exist in finite form. It's decimal does not repeat and does not end. Like pi, it goes on into infinitely more precise values, never reaching exactly 2.00000... when squared.

That's not to even mention the square root of a negative number, which get's us into the realm of complex numbers.

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