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 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 zero
o 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 Zero
o 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