5. Babylonians• First civilization to use zero• Used zero only as a placeholder, never on its own
6. Mayans• First civilization to actively use zero in equations• Used zero to create Long Count and yearly calendars
7. Indians• First civilization to describe the basic mathematical properties of zero• Described addition, subtraction, multiplication, and division with, by, to, and from zero
8. Math with Zero!• 2+0=2• 5–0=5• 4x0=0• 3/0 = ?Which one of these is not like the others?
9. The Powers of Zero!5² = 5 x 5 = 255³ = 5 x 5 x 5 = 125BUT! Why does: 5: = 1?5: = 5 ….???!!
10. The Powers of Zero (Cont’d)5² = 5 x 5 = 255³ = 5 x 5 x 5 = 125What about 5³ x 5²?5³ x 5² = (5 x 5 x 5) x (5 x 5) = 125 x 25 = 3125 there are five 5’s! So: 5³ x 5< = 5⁵ OR!5³ x 5< = 5=⁺< = 5⁵
11. The Powers of Zero (Cont’d – last slide on this I swear!)What about 5³/5<? Well …5³ = 5 x 5 x 55² = 5 x 5 DIVIDING THEM CANCELS TWO 5’sLeaving you with: 5 or 5¹. So 5³/5< = 5=⁻< = 5;Returning to our 5: issue: We know 5=/5³ = 5: 5³ = 5 x 5 x 55³ = 5 x 5 x 5 125/125 = 1
12. Division by Zero!
13. Original Solutions• Solution 1: X/0 = X• Solution 2: X/0 = Undefined (doesn’t work)• Solution 3: X/0 = InfinityCorrect Answer? Let’s look at each closer.
14. Solution 1: X/0 = X
15. Solution 1: X/0 = X (Cont’d) May I have zero slices please?
16. Solution 2: X/0 = Undefined (Doesn’t work)• The standard accepted solution in school and on calculators
18. Solution 3: X/0 = Infinity• Proposed by the Indian mathematician Bháskara• Initially rejected by the mathematical community because of flaws in the proof• Bháskara made an edit that would become the basis for quantum mechanics
19. Solution 4: 0/0 = Infinity• This solution works!Let’s say 0/0 = 746.345689 So if we multiply each side by 00 x 0/0 = 746.345689 x 00=0 Works no matter what number we0/0 = -45078932 set 0/0 equal to!0 x 0/0 = -45078932 x 00=0 Therefore 0/0 = ∞
20. Applications of Solution 4 Quantum Mechanics! Before you look for an electron, it isn’t in any one place – it exists only as a potential. So, it, theoretically, is in an infinite number of locations at any time.
21. Human ApplicationBefore you start anything, your speed –how fast you are moving towards yourgoal – is infinite.
Be the first to comment