- #1
Mépris
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1. Homework Statement :
Show that if a < 0, hen -a > 0
N/A
3. The Attempt at a Solution :
Assume the result is false.
Thus, by trichotomy:
i)
-a = 0
This is not possible. A real number can be greater than zero, less than zero or equal to zero.
Since it has been given that -a > 0, it follows that -a ≠ 0
ii)
-a < 0
If -a < 0, then a > 0
a + (-a) < 0 + a
[itex]\Rightarrow[/itex] a > 0, which is not true!
Since, it is given that a < 0
---
This is my first foray into learning calculus in a more rigorous fashion. I've never done any proofs before. This seems okay to me but it is possible that there is something wrong somewhere. So, is this indeed correct or did I miss something?
Thank you
Show that if a < 0, hen -a > 0
Homework Equations
N/A
3. The Attempt at a Solution :
Assume the result is false.
Thus, by trichotomy:
i)
-a = 0
This is not possible. A real number can be greater than zero, less than zero or equal to zero.
Since it has been given that -a > 0, it follows that -a ≠ 0
ii)
-a < 0
If -a < 0, then a > 0
a + (-a) < 0 + a
[itex]\Rightarrow[/itex] a > 0, which is not true!
Since, it is given that a < 0
---
This is my first foray into learning calculus in a more rigorous fashion. I've never done any proofs before. This seems okay to me but it is possible that there is something wrong somewhere. So, is this indeed correct or did I miss something?
Thank you