Why is 1/0 = oo10=∞ ?
2 Answers
You can fit infinite zeroes into any number
Explanation:
When dividing, you are specifying how may parts of the denominator can fit into the numerator. Therefore, you can fit infinite
Explanation:
So if
Now if
So if
So whether
So what is
It's used in various ways, but often as a shorthand for 'unlimited'.
For example, we speak of the limit as
So we might write:
lim_(n->oo) 1/n = 0
Usually, we also have a negative infinity
lim_(n->-oo) 1/n = 0
...referring to the limit as
We can imagine
The symbols
For example, we could write:
lim_(x->oo) x^2 = +oo
meaning that as
We also find:
lim_(x->0) 1/x^2 = +oo
meaning that as
There are also one sided limits. If we want to speak of the limit as
lim_(x->0+) 1/x = +oo
or from the 'left' (i.e.
lim_(x->0-) 1/x = -oo
So notice that the left and right limits are in stark disagreement about what value we might try to give
When
There are a couple of contexts in which it's meaningful to speak of
They are called the Projective Line