Please follow the following arguments. 5/3=1.66 5/2=2.5 5/1=5 5/0.5=10 ..... .... 5/0=infinity and then 5/(-1)= -5 What you see? As the denominator is decreased the right hand side answer increases. The denominator becomes 3 then 2,then 1, then 0,then -1 ; and the answer increases, therefore -5 must be grater than infinity. Where's the flaw. Please illustrate.
The curve 5/x is an example of a rectangular hyperbola. It's an asymptotic curve. http://en.wikipedia.org/wiki/Asymptote http://mathworld.wolfram.com/Asymptote.html
As one divides by smaller and smaller numbers, the output figure approaches but does not reach infinity, no?
Please follow the following arguments. 5=5 4=4 3=3 2=2 1=1 0=0 -1=-1 What do you see? As the left hand side decreases, the right hand side is greater than or equal to zero. Therefore, -1 must be greater than or equal to zero. Ja? Just because a property holds true for a certain range of numbers, it doesn't mean the pattern will follow for numbers outside that range. That's the flaw.
In absolute value, yes. But else you have to mind the sign, depending on whether you're approaching 0 from the left or right, you get -inf resp. +inf.
I don't see how you can say that -1 is greater than or equal to 0. I might be horribly wrong but what I think you're doing is just equating numbers & two equal numbers are always equal .. under no circumstances can be greater than or equal to. Look at this order: 1=1 9=9 8=8 -1=-1 Don't you see?
Albert: Please follow the following arguments. (x^2=y) 3^2=9 2^2=4 1^2=1 0^2=0 -1^2=1 What you see? As the x value is decreased, the y value (right hand side answer) decreases. The x value becomes 3 then 2,then 1, then 0,then -1 ; and the answer (y) decreases, therefore 1 must be less than zero. Now where's the flaw? (Hint: the only flaw is the conclusion that a given function must result in a straight and continuous line.)
Okay...let me try to hit this topic. Graphing 5/x you will have a line that going from negative infinity to positive infinity it ALWAYS DECREASES. it never increases. However, it starts out negative and ends up positive. Lesson learned today: Don't mess with the division by zero.
No you do not have a line. You have a hyperbola in the first and third quandrants of the cartesian plane.