Ryan SemeradUnderstanding Nothing

This Page Intentionally Left Blank

Do you understand nothing?

The History of Nothing (Zero)

Babylonians

• First civilization to use zero• Used zero only as a placeholder, never on its

own

Mayans

• First civilization to actively use zero in equations

• Used zero to create Long Count and yearly calendars

Indians

• First civilization to describe the basic mathematical properties of zero

• Described addition, subtraction, multiplication, and division with, by, to, and from zero

Math with Zero!

• 2 + 0 = 2• 5 – 0 = 5• 4 x 0 = 0• 3/0 = ?

Which one of these is not like the others?

The Powers of Zero!

5² = 5 x 5 = 255³ = 5 x 5 x 5 = 125

BUT! Why does: 5⁰ = 1?

5⁰ = 5 ….???!!

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 5² = 5⁵OR!

5³ x 5² = 5³⁺² = 5⁵

The Powers of Zero (Cont’d – last slide on this I swear!)

What about 5³/5²? Well …5³ = 5 x 5 x 55² = 5 x 5 DIVIDING THEM CANCELS TWO 5’sLeaving you with: 5 or 5¹. So 5³/5² = 5³⁻² = 5¹Returning to our 5⁰ issue: We know 5³/5³ = 5⁰ 5³ = 5 x 5 x 55³ = 5 x 5 x 5 125/125 = 1

Division by Zero!

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.

Solution 1: X/0 = X

Solution 1: X/0 = X (Cont’d)

May I have zero slices please?

Solution 2: X/0 = Undefined (Doesn’t work)

• The standard accepted solution in school and on calculators

Solution 2: X/0 = Undefined (Cont’d)

A ≠ BA x 0 = 0B x 0 = 0A x 0 = B x 0A x 0 = B x 0 0 0A = B

OR

2 ≠ 32 x 0 = 03 x 0 = 02 x 0 = 3 x 02 x 0 = 3 x 0 0 02 = 3

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

Solution 4: 0/0 = Infinity

• This solution works!Let’s say 0/0 = 746.3456890 x 0/0 = 746.345689 x 00 = 0

0/0 = -450789320 x 0/0 = -45078932 x 00=0

So if we multiply each side by 0

Works no matter what number we set 0/0 equal to!

Therefore 0/0 = ∞

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.

Human Application

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

Ryan Semerad

Thank You!