Table of Contents
What happens when you add infinity to infinity?
is not a number. If you add one to infinity, you still have infinity; you don’t have a bigger number. If you believe that, then infinity is not a number.
Is infinity and infinity same?
the Russian mathematician Ludwig Phillip Cantor demonstrated that there are an infinite number of numbers just between 0 and 1 and more than one kind of infinity – the countable and the uncountable: infinity equals infinity equals infinity and independent of dimension, as the mind-defying proposition goes.
Can you do math with infinity?
Most students have run across infinity at some point in time prior to a calculus class. However, when they have dealt with it, it was just a symbol used to represent a really, really large positive or really, really large negative number and that was the extent of it.
Does Infiniti have a beginning?
Most infinities do have beginnings, simply because in order to tangibly grasp the concept of whatever infinity we are talking about (just based on the limitations of the human mind) we generally need a starting point.
What does it mean when someone says the limit is infinity?
Now a limit is a number—a boundary. So when we say that the limit is infinity, we mean that there is no number that we can name. The student should be aware that the word infinite as it is used and has been used historically in calculus, does not have the same meaning as in the theory of infinite sets.
What does it mean to say that something is infinite?
When we say in calculus that something is “infinite,” we simply mean that there is no limit to its values. Let f ( x ), for example, be . Then as the values of x become smaller and smaller, the values of f ( x) become larger and larger.
When does a variable become infinite or tend to infinity?
We say that a variable “becomes infinite” or “tends to infinity” if, beginning with a certain term in a sequence of its values, the absolute value of that term and of any subsequent term we name is greater than any positive number we name, however large. When the variable is x and takes on only positive values, then x becomes positively infinite.
How do you read the limit as x approaches infinity?
We should read that as “the limit as x becomes infinite,” not as ” x approaches infinity” because again, infinity is neither a number nor a place. On the other hand, we could read that however we please (“the limit as x becomes dizzy”), as long as whatever expression we use refers to the condition of Definition 4.