The dot is open, if it is less than or equal to than the dot is closed
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Well, honey, if the inequality is strictly greater than, like ">", then it's an open dot because that endpoint ain't included in the solution. But if it's greater than or equal to, like ">=", then you better believe it's a closed dot because that endpoint is part of the party. Hope that clears things up for ya!
a solid dot is , if less tha or equal to, or grearter than or just greater than and less than.
If the inequality includes 'or equal' then use a solid dot [the value is included]. If it doesn't use 'or equal' then use the open dot.
Thin of the number line with a solid dot on the number -4. Everything to the left of your dot satisfies real numbers less than or equal to 4. The set it infinite, of course. In set builder notation, {x: x< or = 4}
A line which has one end, but stretches off to infinity is called a ray. If we want to show an interval such as [2,infinity) which means all the numbers between two an infinity including two, we put a close dot at two and draw a ray going to the right. Similarly for (negative infinity, 2] we draw the closed dot at 2 but this time the ray goes to the left. Now if we draw an open circle, or a the out line of a dot this mean the interval (2,infinity) where we are considering all the numbers very close to two but not two itself This is an open half line and it represents an open interval.