Shall I compare thee to a summer's day?
Thou art more lovely and more temperate.
Rough winds do shake the darling buds of May,
And summer's lease hath all too short a date.
Sometime too hot the eye of heaven shines,
And often in his gold complexion dimm'd;
And every fair from fair some time declines,
By chance, or nature's changing course, untrimm'd;
But thy eternal summer shall not fade
Nor lose possession of that fair thou ow'st;
Nor shall death brag thou wand'rest in his shade,
When in eternal lines to time thou grow'st.
So long as men can breathe or eyes can see,
So long lives this, and this gives life to thee.
I didn't like Shakespeare until I've read this, either.
Some time ago I claimed that y/0=∞ . Now, though, I really delved into it. Let us say easily that y=1 , works, right? So, 1/0 . But, in Calculus, we need limits. What we get here is a Point. Let's make it so it will have limits: 1/x .
Cool. Now that we have that, let's make a graph: f(x)=1/x . I used this program.
(For the time being, let's ignore the left Hyperbola [the "tinted parabola"]) What we got here is an Hyperbola, and when x gets close to 0, the value of x gets so big, that it grows beyond bounds. Zoom out to m(20,20) and m(-20,-20) and you can see that the Hyperbola almost touches the y-axis, but it doesn't. Ever. That's what we call an Infinity.
Seemingly, now, I was right. BUT BUT BUT, look at the left Hyperbola. It is the negative form of the previous Hyperbola. So, by setting our limits as we should in Calculus, the answer for y/0 is ±∞ . Pretty big? Yes.
Just one problem. In Algebra and Arithmetic, when we say Infinity, it really doesn't mean anything. Seemingly it does, but infinities don't grow or shrink. They are a constant, and they are also an Irrational Number(=a number the human brain cannot comprehend. Try thinking about what Infinity is, and you'll know what I mean. Or for that matter, the square root of 2 or pi), and when you actually multiply both sides of an equation by Infinity, it doesn't make sense. You changed the value of Infinity. That's a no no, as Infinity is not a variable. You can change x and y and all others, but you can't change the values of 2 or 89 or Infinity.
So again, I apologize. As shown above, upon division by zero, you get to something that cannot be comprehended and doesn't make any sense, in the way of using it.
For all those confused as to the connection of 1/0 and infinity on the graph: Let us just say that where the Hyperbola ends, in Infinity (of course), it touches the y-axis, making that point (0,∞) .