Can you find a number that lies one third of the distance between 1/3 and 2/3?

I know a number which is spelt in alphabetical order.
Do you?

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth, the other always lies and you don't know which is which.
What is the question you ask?

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

I can prove why 1 = 2

* Lets say y = x
* Multiply through by x xy = x2
* Subtract y2 from each side xy - y2 = x2 - y2
* Factor each side y(x-y) = (x+y)(x-y)
* Divide both sides by (x-y) y = x+y
* Divide both sides by y y/y = x/y + y/y
* And so... 1 = x/y + 1
* Since x=y, x/y = 1 1 = 1 + 1
* And so... 1 = 2

How is this possible?

Can you make four (4) nines (9) equal 100?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

Take one out and scratch my head, I am now black but once was red. What am I?

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

What does this rebus photo means?