The discussion revolves around the concept of absolute value in mathematics, specifically addressing the question of how the absolute value of a number can be perceived as negative in certain contexts. Participants are examining the definitions and implications of absolute value as presented in a textbook, particularly in relation to the triangle inequality.
The discussion is progressing with participants clarifying their understanding of absolute value. Some have offered insights that help others grasp the relationship between negative values and their absolute counterparts. There is a recognition of the need to reconcile definitions with examples, indicating a productive exploration of the topic.
Participants are grappling with the definitions provided in the textbook, which may not align with their initial interpretations. The discussion highlights the importance of understanding the conditions under which absolute values are defined and the potential for confusion in their application.
The absolute value would still be positive? Isn't the point of absolute value to obtain positive results only?vela said:Your interpretation is only true if you're assuming x>0. What if x itself is negative?
1. How does that explain the definition given though? It says |x| = -x if x<0. So by his definition, if I say x = -3, |x| = |-3| = -3.vela said:If ##x=-1##, what's ##-x## equal to?
Ohhh. I understand it now. |-3| = -(-3) = 3.vela said:If ##x=-1##, what's ##-x## equal to?