Ryan presents on understanding zero, and its origins.

2. Ryan Semerad
Understanding Nothing

3. This Page Intentionally Left Blank

4. Do you understand nothing?

5. The History of Nothing (Zero)

6. Babylonians
• First civilization to use zero
• Used zero only as a placeholder, never on its
own

7. Mayans
• First civilization to actively use zero in
equations
• Used zero to create Long Count and yearly
calendars

8. Indians
• First civilization to describe the basic
mathematical properties of zero
• Described
addition, subtraction, multiplication, and
division with, by, to, and from zero

9. Math with Zero!
• 2+0=2
• 5–0=5
• 4x0=0
• 3/0 = ?
Which one of these is not
like the others?

10. The Powers of Zero!
5² = 5 x 5 = 25
5³ = 5 x 5 x 5 = 125
BUT! Why does: 5: = 1?
5: = 5 ….???!!

11. The Powers of Zero (Cont’d)
5² = 5 x 5 = 25
5³ = 5 x 5 x 5 = 125
What 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

12. The Powers of Zero (Cont’d – last slide
on this I swear!)
What about 5³/5<? Well …
5³ = 5 x 5 x 5
5² = 5 x 5 DIVIDING THEM CANCELS TWO 5’s
Leaving 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 5
5³ = 5 x 5 x 5 125/125 = 1

13. Division by Zero!

14. Original Solutions
• Solution 1: X/0 = X
• Solution 2: X/0 = Undefined (doesn’t work)
• Solution 3: X/0 = Infinity
Correct Answer? Let’s look at each closer.

15. Solution 1: X/0 = X

16. Solution 1: X/0 = X (Cont’d)
May I have zero slices
please?

17. Solution 2: X/0 = Undefined (Doesn’t
work)
• The standard accepted solution in school and
on calculators

18. Solution 2: X/0 = Undefined (Cont’d)
A≠B 2≠3
Ax0=0 2x0=0
Bx0=0 3x0=0
2x0=3x0
Ax0=Bx0 OR 2x0=3x0
Ax0=Bx0 0 0
0 0 2=3
A=B

19. 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

20. Solution 4: 0/0 = Infinity
• This solution works!
Let’s say 0/0 = 746.345689 So if we multiply
each side by 0
0 x 0/0 = 746.345689 x 0
0=0
Works no matter
what number we
0/0 = -45078932 set 0/0 equal to!
0 x 0/0 = -45078932 x 0
0=0 Therefore 0/0 = ∞

21. 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.

22. Human Application
Before you start anything, your speed –
how fast you are moving towards your
goal – is infinite.

23. Thank You!
Ryan Semerad