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Zero: Infinity’s Twin
By Travis Mackoy
Life Without Zero
o Zero was not needed in primitive societies
o Mathematics was originally “one” or “many”
o 30,000 year old Czechoslovakian wolf bone found with notches, indicating counting.
Babylonians
Used a sexagesimal system,based on the number 60.
Greeks
o The Greek mathematical system was based on geometry and did not need zero as a placeholder, or as a stand alone number.
o The Greeks would share astronomical data with the Babylonians and therefore knew about the placeholder zero, but as a number it would not be accepted.
Hindus
o The Hindus in India did not fear zero as the Greeks did
o Brahmagupta, an Indian mathematician, first worked on the properties of zero as a stand alone number in the 7th century.
o “The sum of a positive number and zero is positive…the sum of a negative number and zero is negative.
o Zero divided by zero is zero.o n divided by zero is n/0 and zero divided by n is
0/n.
Hindus
o The Hindus in India did not fear zero as the Greeks did
o Brahmagupta, an Indian mathematician, first worked on the properties of zero as a stand alone number in the 7th century.
o “The sum of a positive number and zero is positive…the sum of a negative number and zero is negative.
o Zero divided by zero is zeroo n divided by zero is n/0 and zero divided by n is
0/n.
Hindus
o The Hindus in India did not fear zero as the Greeks did
o Brahmagupta, an Indian mathematician, first worked on the properties of zero as a stand alone number in the 7th century.
o “The sum of a positive number and zero is positive…the sum of a negative number and zero is negative.
o Zero divided by zero is zeroo n divided by zero is n/0 and zero divided by n is
0/n.
Hindus Cont.
o Mahavira writes a book in the 9th century as an update to Brahmagupta’s book.
o A number multiplied by zero is zero.
o A number remains unchanged when divided by zero.
Hindus Cont.
o Mahavira writes a book in the 9th century as an update to Brahmagupta’s book.
o A number multiplied by zero is zero.
o A number remains unchanged when divided by zero.
Hindus Cont.
o Mahavira writes a book in the 9th century as an update to Brahmagupta’s book.
o A number multiplied by zero is zero.
o A number remains unchanged when divided by zero.
Hindus III
o In the 14th century, Bhaska writes a book continuing to try to explain the mathematical properties of zero.
o Zero squared and the square root of zero are zero.
o He concludes that n/0 = infinity.
Hindus III
o In the 14th century, Bhaska writes a book continuing to try to explain the mathematical properties of zero.
o Zero squared and the square root of zero are zero.
o He concludes that n/0 = infinity.
Hindus III
o In the 14th century, Bhaska writes a book continuing to try to explain the mathematical properties of zero.
o Zero squared and the square root of zero are zero.
o He concludes that n/0 = infinity.
Islamic Influence
o Al-Samawal writes:
o If we subtract a positive number from zero, the same negative number remains…
o If we subtract a negative number from zero, the same positive number remains.
Islamic Influence
o Al-Samawal writes:
o If we subtract a positive number from zero, the same negative number remains…
o If we subtract a negative number from zero, the same positive number remains.
Cardan
o Italian mathematician in the 16th century that solved cubic and quartic equations without using zero!
o It wouldn’t be until the 18th century that the number zero began to enjoy widespread use.
Where nature divides by Zeroo According to Charles
Seife:o A black hole is a zero in
the equations of general relativity.
o The energy of the vacuum is a zero in the mathematics of quantum mechanics.
o The big bang is a zero in both theories.
Zero Destroys Mathematics
