How Much Is Infinity?

How Much Is Infinity? — page 3 — THE ANCIENT EGYPTIANS MADE THEIR HOME ALONG THE NILE RIVER OPPOSITE 6

How Much Is Infinity? — page 4 — BASICS OF BASE-10 WHEN DID YOU START using math It was probably when you learned to count You started by counting to 10 and then to 100 Next you learned how to write numbers That is the same process people have used for thou sands of years They began by counting everyday objects and then wrote numbers to share their counts with others One of the most basic systems for writing numbers was the tally system In this system a tally mark represents the number one It is easy to understand at first but can quickly become difficult to follow as larger numbers require many tallies Therefore it eventually became necessary to find ways to shorten nu meric representations One of the earliest civilizations to have a written language the Egyptians wrote their numbers just like they wrote everything else with pictures called hieroglyphs Some of the pictures make sense to us like using a tally for the num ber one Others seem a little strange such as the astonished man that represents 1,000,000 In hieroglyphs the number 1,126 would be written like this 7

How Much Is Infinity? — page 5 — As new civilizations rose to power in the regions around Egypt they de veloped different writing systems and eventually alphabets Different soci eties developed their own number systems which involved unique symbols and counting methods Between 2000 and 200 b c in the area known as Mesopotamia present-day Iraq the Babylonian system originated were determined by their order or place Instead of base-10 the Babylonians used a sexigesimal system which is similar to what we use to divide 1 minute into 60 seconds They used symbols called wedges to represent 1 The Babylonians used a place value system in which symbols values and 10 All the numbers were written using a combination of those two wedges Then they were grouped to show their position in base-60 To write 1,126 you would do this The development of number systems was not limited to western Eu rope and Asia Across the ocean the Maya used a place value system based on the number 20 The Maya used a ____ for the number 5 and to represent 1 They were the first to use a symbol for zero Mathematicians in other parts of the world struggled with how to represent zero They did not understand why they would need a symbol for nothing However the Maya saw its usefulness when a certain place had no quantity represented in it The most common Maya representation for zero was a shell Because the Maya were so far away their number system did not impact the mathe maticians of Europe though 8

How Much Is Infinity? — page 6 — Instead ancient Romans had the greatest influence on Western math The Romans be gan using what we recognize as letters for their numbers in the 7th century b c There are two main theories about the origin of Roman numer als The first relates to the previously mentioned tally system In the Roman tally system every 5th tally was double-marked V or and every 10th tally was crosscut X It is argued that the basic Roman numerals for 1 5 and 10 come from this process The second theory involves hand signals such as holding up one finger to mean 1 Although neither explanation refers to letters exactly it is easiest to discuss Roman numerals EQUALS E T U N I M by referencing the individual letters used Unlike the Babylonian and Maya place value systems the Romans used an additive system A number’s value came from adding the values represented by each letter There is also a subtraction component to this system To avoid writing one number more than four times the smaller number is placed in front of the bigger number to show subtraction The number nine for instance was written as IX to signify 10 minus 1 And 99 had to be written as XCIX XC for 90 and IX for 9 Roman numerals may have looked more like a spelling test but the Romans were able to write every number except zero 9

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