Algebraic Set Query: Can a Take Any Value?

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Discussion Overview

The discussion revolves around the equation a=bx, where x is a real constant and b can take any value. Participants explore whether a can take any value under these conditions, particularly focusing on the case when x is not equal to zero.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if a can take any value if b is unrestricted and x is a constant.
  • Another participant suggests drawing the graph for further insight, implying a visual approach may clarify the situation.
  • A third participant acknowledges that if x equals zero, then a must also equal zero, but raises the question of the scenario when x is not zero.
  • One participant asserts that a can take any value as long as x is not zero, reiterating the initial query.

Areas of Agreement / Disagreement

There is no clear consensus; while some participants suggest that a can take any value when x is not zero, others raise questions and provide different perspectives on the implications of x being zero.

Contextual Notes

The discussion does not resolve the implications of the relationship between a, b, and x, particularly regarding the case when x equals zero versus when it does not.

Big-Daddy
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If a=bx, where x is a real constant and b can take literally any value, can a always take literally any value?
 
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Draw the graph (for x != 0) and tell us what you think.
 
OK fine, that's a trivial case. a=0 if x=0 regardless of b. For all x where x is not equal to 0?
 
Big-Daddy said:
If a=bx, where x is a real constant and b can take literally any value, can a always take literally any value?

Yes, as long as x is not 0.
 

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