consider the graph below which is
y = 1/x. Then ask the question: where does this graph touch the x axis? The answer is both + infinity and - infinity. In other words the reciprocals of + and - infinity are both zero, causing + and - infinity to look as being equal.
Another interesting way of viewing this is as follows:
Many graphs are continuous, i.e. there is one line continues without breaking. However this graph is discontinuous at the x and axes which it never meets …… until + or - infinity.
Now a way of looking at how these two separate parts of this hyperbola could join to make one continuous line would be to look at the x and y axes as being curved (with an infinite radius) to ultimately join up. If this occurred then -infinity would join up with +infinity on both axes, and the graph would be a continuous function in both vertical and horizontal directions.
In some ways it is a natural way to look at it, as it is said that space is curved anyway, so in reality + and - infinity seem to be the same thing.
