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Zero : when empty became a number

Zero : when empty became a number. Definition. The number zero is a mathematical object which expresses a absence : it is the number of elements of the empty set. It is the smallest integer . History of the number zero. A late invention

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Zero : when empty became a number

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  1. Zero :whenemptybecame a number

  2. Definition The numberzerois a mathematicalobjectwhichexpresses a absence : itis the number of elements of the empty set. It is the smallestinteger.

  3. History of the numberzero A late invention - 0 : which represents the empty, was difficult to see for some civilizations which rejected the notion of nothingness. - It was the case for Greek philosophers : Aristote thought that the empty didn’t exist and that it was useless and even wrong to name it. .

  4. The apparition of the zero • 0 : invented by Babylonians three centuries before Jesus. • Babylonians : - used a numerotation system very complex, • - first to create a symbol (two chevrons angled ) to indicate the absence of unit. They always appear inside the number (like into the zero in 205).  • But this zero was not used to do calculations, it was not considered as a number.

  5. The evolution of the zero - in India (in the fifth century) : appears the modern function of the zero as a number. Contrary to Babylonians, Indians used the zero as a number to indicate the absence but also to do arithmetics. - This number has been defined by the mathematicianBrahmagupta (628), in his tract : « Brahmasphutasiddharta », as a subtraction of a number by itself : a-a = 0 and hewritesitsproperties: - a + 0 = a - a – 0 = a - a x 0 = a He affirmsthatdividing by zerois a definition of infinite. That iswhywecan’tdivide by zero.

  6. - 0 : was represented by a cercle and was called “sunya” => “empty”. - indiannotion and notation of the zero were taken by arabs mathematicians during the ninth century. - It is in the twelth century that the use of the zero is shared by all the Occident, thanks to the translation of the book of the mathematcian Al-Kuvarizhmi. A decisive progress The invention of the zero was a very important step for the mathematical’s history. Thanks to the zero, negative numbers were invented.

  7. MathematicalProperties • 0 : whenzeroisalone : itindicatesnothing • 105 & 15 : zero notes the emptyplace • 24  240 : zeroatleftmeansthat the numberismultiplied by 10 • ...-2, -1, 0, 1, 2,… : zerois the transition between positive numbers and negativenumbers

  8. Zeroiseven : - A number n iseven, if itexists a number k such as n=2k With k=0, n = 2 x 0 = 0 => 0 iseven - A numberiseven if itcanbedivide by 2, whichmeansthat the remainderiszero 0 divided by 2 gives a remainder of 0 => 0 iseven - The sum of twoevennumbersiseven.     0 + 2 = 2 => correct with0 => 0 iseven

  9. Zerois not a prime number: A prime numbercanbeonlydivided by 1 and by itself. But 0 is divisible by everynumber(whichgives 0), exept by 0  So zerois not a prime number

  10. Zerois a round number Hey, you have a new belt ! :D

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