- #1
Phylosopher
- 139
- 26
< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >
I couldn't find more informative title!
I find difficulties with proofs. So my solution might be weird
The problem says
"Suppose that x is a fixed non-negative real number such that, for all positive real numbers ε, 0≤ε<x. Show that x=0."
My attempt was:
Assume 0≤x and x <ε
Case 1:
0 <x
For evey ε, 0<x and x <ε is false
Case 2:
0=x
For evey ε, 0=x and x <ε is trueMy professor was not happy with making cases to proof the statement, and he said this is not a real proof. He suggested starting with the assumption 0 <x and from that I proof 0=x is the wanted fixed non negative real number that satisfies the statement.
I am confused. How am I supposed to proof it?
I couldn't find more informative title!
I find difficulties with proofs. So my solution might be weird
The problem says
"Suppose that x is a fixed non-negative real number such that, for all positive real numbers ε, 0≤ε<x. Show that x=0."
My attempt was:
Assume 0≤x and x <ε
Case 1:
0 <x
For evey ε, 0<x and x <ε is false
Case 2:
0=x
For evey ε, 0=x and x <ε is trueMy professor was not happy with making cases to proof the statement, and he said this is not a real proof. He suggested starting with the assumption 0 <x and from that I proof 0=x is the wanted fixed non negative real number that satisfies the statement.
I am confused. How am I supposed to proof it?