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Homework Statement:
 Prove that a=a
Relevant Equations:

##a= a, ## if ## a \geq 0 ## and
a, if ## a \leq 0 ##
Problem Statement: Prove that a=a
Relevant Equations: ##a= a, ## if ## a \geq 0 ## and
a, if ## a \leq 0 ##
Somewhat stumped on where to start....
i know that we need to use cases. If we consider ##a\geq 0##, then are we allowed to use the fact that ##a=1\cdota = a ##?
This is from Spivak so in the P1 to P12, and triangle inequality, the above has not been developed.
What about using the triangle inequality? But how would we separate ##aa##?
Any input would be greatly appreciate! Thank you in advance
Relevant Equations: ##a= a, ## if ## a \geq 0 ## and
a, if ## a \leq 0 ##
Somewhat stumped on where to start....
i know that we need to use cases. If we consider ##a\geq 0##, then are we allowed to use the fact that ##a=1\cdota = a ##?
This is from Spivak so in the P1 to P12, and triangle inequality, the above has not been developed.
What about using the triangle inequality? But how would we separate ##aa##?
Any input would be greatly appreciate! Thank you in advance