can someone help me with this one?
1) the function has a upper limit but then i get lost.. don't know what f(0) = 0 means.. is it a minimum (inf)?
2) no clue.. injective function?
3) ∃λ ∈ ℝ. a = λ b ; a ≠ 0,b ≠ 0, λ ≠ 0 maybe?
1) says that no matter how close you are from in there is always a lower positive real number where the function nullifies. Example:
2) This is not injectivity: for instance, consider the constant function equal to Then for all so " " is true. But of course is not injective.
Assume there are two different reals where value is Is the formula true? Conclude.
This is wrong because if and that would mean a and b are not linear dependent, when they are.∃λ ∈ ℝ. a = λ b
You have no condition about and so they can be the zero vector. To say are linearly dependent, use two scalars in your formula, or consider two cases: one with and the other with