1. The surface of the moon is

1 unbounded and infinite.
2 bounded and infinite.
3 unbounded and finite.
4 bounded and finite.

2. I prove in 6 steps that 1+1 = 1. Or did I make a mistake?

1. x = x (certainly correct)
2. x²-x² = x²-x² (multiply by x, then subtract x² on both sides)
3. x²-x² = x∙(x-x) (right: move x out of the brackets)
4. (x+x)∙(x-x) = x∙(x-x) (left: a²-b² = (a+b)∙(a-b) )
5. (x+x) = x (eliminate the factor (x-x) on both sides)
6. 1+1 = 1 (let x = 1)

1 Step 1 is wrong.
2 Step 2 is wrong.
3 Step 3 is wrong.
4 Step 4 is wrong.
5 Step 5 is wrong.
6 Step 6 is wrong.
7 All steps are correct but the conclusion is wrong.

3. The radius of the universe is about

1 ~13.7 billion light years.
2 ~46 billion light years.
3 ~78 billion light years.
4 even greater.

4. The first hazard to render earth unsuited for life will be

1 Collision of the Milky Way with the Andromeda Galaxy.
2 Evaporation of the oceans.
3 Collision of the earth with the moon.
4 Inflation of the sun to a Red Giant.
5 Shrinking of the sun to a White Dwarf.

5. A writer starts writing his memories. He needs a week for covering a single day of his life. So every week he gets 6 more days to write about. Even if he's immortal, will he ever be able to cover his entire life in his memories?

1 Yes.
2 No.

6. Which of the following statements is true?

1 There are more natural numbers than odd numbers.
2 There are more fractions than integers.
3 There are more real numbers than rational numbers.
4 All of the above.
5 None of the above.

7. A feminist editor revises a text by replacing every appearance of the letters "man" with "woman". So "man and woman" becomes "woman and wowoman" after the revision. Can full equality of man and woman be achieved in the text?

1 Yes, after one revision.
2 Yes, after two revisions.
3 Yes, after infinite many revisions.
4 No.

8. Suppose ω is the smallest number that is greater than any finite number. Which number is even greater than ω?

1 ω+1
2 2∙ω
3 1+ω
4 All of the above.
5 None of the above.