quadrant
- Thread starter ggrove
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pka
Elite Member
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- Jan 29, 2005
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“necessary and sufficient conditions for inequalities to represent an area in the first quadrant”
Your question is somewhat ambiguous.
But I will assume that you are asking about a solution set of a system of inequalities.
Also, assuming that by ‘an area’ you mean a bounded region and the area is finite.
If S={(x,y)} is the solution set then x≥0 and y≥0, first quadrant.
Moreover, {y|(x,y)εS for some x} is bounded above and {x|(x,y)εS for some y} is also bounded above.
In other words, the sets of x & y is the solution are both bounded.
Your question is somewhat ambiguous.
But I will assume that you are asking about a solution set of a system of inequalities.
Also, assuming that by ‘an area’ you mean a bounded region and the area is finite.
If S={(x,y)} is the solution set then x≥0 and y≥0, first quadrant.
Moreover, {y|(x,y)εS for some x} is bounded above and {x|(x,y)εS for some y} is also bounded above.
In other words, the sets of x & y is the solution are both bounded.