Zero

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This is a slide show on the concept of Zero in Mathematics and how it relates to the parallel concept of Nothing in Theology and Philosophy.

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Zero

  1. 1. Zero: 0 “In the history of culture, the discovery of zero will always stand out as one of the greatest single achievements of the human race.” Tobias Danzig WITHOUT ZERO: • THERE WOULD BE NO CALCULUS. • NO FINANCIAL MATHEMATICS. • NO ALGEBRA • NO ABILITY TO DO CALCULATIONS QUICKLY. • NO COMPUTERS. 5/13/2014 1
  2. 2. ZERO IS A SPECIAL NUMBER • IF WE ADD ZERO TO ANY NUMBER THE RESULT IS THE ORIGINAL NUMBER. A + 0 = A •(THE SAME IS TRUE FOR SUBTRACTION). A – 0 = A • IF YOU MULTIPLY ANY NUMBER BY ZERO THE PRODUCT IS ZERO. A x 0 = 0 •IF YOU RAISE ANY NON-ZERO NUMBER TO THE POWER OF ZERO, THE RESULTING NUMBER IS 1: Aº = 1 • IF YOU DIVIDE ZERO BY ANY NON-ZERO NUMBER, THE QUOTIENT IS ZERO. 0 ÷ A = 0 • ANY NUMBER DIVIDED BY ZERO IS UNDEFINED. A ÷ 0 is UNDEFINED 5/13/2014 2
  3. 3. Error: Division by Zero The error here is the division by (a-b) which is ZERO which is an operation that is inadmissible in mathematics. 5/13/2014 3
  4. 4. A Brief History of ZERO •The Maya civilization (2000 B.C. – 900 A.D.) in what is now Mexico used the concept of zero as a PLACEHOLDER: that is, 705 is a way bigger number than 75. (Like using a comma in written language.) The Babylonians used it similarly in the 7th century B.C. • The 7th century Indian mathematician Brahmagupta treated zero as a “number” and not just as a place-holder. He elaborated the rules mentioned on page 2 of this presentation. • The Hindu-Arabic numbering system that included zero in the way that was used in the West by Leonardo of Pisa – Fibonacci - in his Book of Counting, published in 1202. • Zero gained a central place in the number system soon afterwards, with it literally separating the positive numbers from the negative ones as in the number line. • In the decimal system, zero serves as a place holder which enables us to use both huge numbers and microscopic figures. • Hence the sheer beauty and usefulness of zero which could lend its use to science in its wonderfully succinct scientific notation. 5/13/2014 4
  5. 5. ZERO IS NOT NOTHING • LATIN: “cifra” = zero; FRENCH: “chiffre” • In English we use the word “nought” to mean zero, a derivation from the word “nothing.” • However, Nought is really a mathematical misnomer (that is, a wrong name), for it would be wrong to think of zero as nothing. • 0 is certainly SOMETHING: it is a powerful symbol, 0, that gives our modern notation extraordinary power. 5/13/2014 5
  6. 6. Zero as Central Point or Start Point • In the Real Number System, 0 is the only number that is neither negative nor positive. • It holds the unique position, almost the Still Point to use Eastern Philosophy, between the positive numbers and the negative ones. • This position makes 0 the natural starting point or origin on many scales such as on the axes of Cartesian Geometry or Co-ordinate Geometry, or on the many scales used in scientific measurement from Temperature to Air Pressure to Acidity/Basicity etc 65/13/2014
  7. 7. A Little Bit of Religion (Theology) • The mainline Christian religions believe that God created the world out of NOTHING. But there are other viewpoints among different religions that God could have created the world from pre-existing matter (chaos) etc. This contradicts mainline science on the origins of the Universe. • Creation out of nothing, or creation ex nihilo, is the belief that God created the world out of nothing, ex nihilo being Latin for "from nothing." This view does not contradict THE BIG BANG THEORY of the origin of the Universe. So this view can be reconciled with the teachings of science. • Scientists say that there was no time or space, therefore literally nothing, there before the great explosion of THE BIG BANG. • For believers “creation out of nothing” is a religious tenet that shows both the power and mystery of God. 5/13/2014 7
  8. 8. A Little Bit of Philosophy (Wondering)1 • Asking the Big Questions of Life. • “Why is there Something rather than Nothing?” – a question asked by the philosopher Martin Heidegger (1889-1976). • What is some-thing? What is no-thing? • Some mathematicians have said that zero is not “nothing” as it is a very important symbol and indeed a number very necessary to all modern calculations. However, philosophers would say that this is true to some extent only, as zero as a symbol represents “nothing” and that it is important to ask the question as to what that nothing is. • Did I come from Nothing into life and then do I return into Nothing? • Is there a spiritual world there beyond the visible world? Or just Nothing? • Or again, good philosophers of mathematics ask what are numbers anyway? 5/13/2014 8
  9. 9. A Little Bit of Philosophy (Wondering) 2 • Does a hole exist in itself? Is it some-thing or no-thing? • Do letters that are engraved in or cut into solid stone exist in themselves? Something made out of Nothing! • Does the year ZERO, 0, exist? The Year 1 B.C. is actually followed by the year 1 A.D. • Does the floor Zero exist? We call the ground floor no. 1. • What is absolute ZERO? Ask a Chemistry student. • Tacticians speak about zeroing in on a target. • A zero-sum game is one where the loss of one player is balanced by the gain of another or others .e.g., poker where what the winner wins equals what the losers lost. • Is the Stock Market a Zero-Sum game? 5/13/2014 9
  10. 10. Some Final Thoughts • How tiny are you in comparison to the size of the universe? How big is the universe in comparison to you? Is your size actually approaching zero. • Limits are important in algebra and in differentiation: We speak of the limits of certain expressions in x as x approaches ZERO or INFINITY etc. The mathematical principle is that x or y or whatever letter you choose may approach either 0 or Infinity, but never get there. In mathematical terms division by ZERO and INFINITY is undefined. • Limits are always about approaching ZERO or INFINITY but never getting there. • Maybe the Mystery of God is like the Mystery of Zero or the Mystery of Infinity – we can never really understand it in this life – we cannot simply get there through human reasoning. • Let the Wonder of ZERO, 0, begin!! 5/13/2014 10

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