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What exactly is infinity? - Mathematics Stack Exchange Definition: Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics The English word infinity derives from Latin infinitas, which can be translated as " unboundedness ", itself derived from the Greek word apeiros, meaning " endless "
One divided by Infinity? - Mathematics Stack Exchange Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it You can extend those sets to include infinity - but then you have to extend the definition of the arithmetic operators, to cope with that extended set And then, you need to start thinking about arithmetic differently
What is infinity divided by infinity? - Mathematics Stack Exchange I know that $\infty \infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
I have learned that 1 0 is infinity, why isnt it minus infinity? This obviously makes no sense - we say that 0 0 is "undefined" because there isn't really an answer Likewise, 1 0 is not really infinity Infinity isn't actually a number, it's more of a concept If you think about how division is often described in schools, say, number of sweets shared between number of people, you see the confusion
How many different sizes of infinity are there? 24 It's pretty straightforward to say that there is an infinite number of different sizes of infinity, but then I thought, "What size of infinity is that?" My thoughts are that the number of unique cardinalities is equivalent to the number of real numbers, based on the fact that the cardinalities can always be ordered by increasing size
Does the concept of infinity have any practical applications? Absolutely, infinity has countless (:P) practical applications Here's one way to think about it: do negative numbers have any practical applications? I mean you can't really have a negative amount of anything, can you? You can't have negative five apples If your bank balance is negative, that's just another way of saying you owe the bank a (positive amount of) money, rather than the other
definition - Is infinity a number? - Mathematics Stack Exchange For infinity, that doesn't work; under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$ So while for some purposes it is useful to treat infinity as if it were a number, it is important to remember that it won't always act the way you've become accustomed to expect a number to act
When 0 is multiplied with infinity, what is the result? Because multiplying by infinity is the equivalent of dividing by 0 When you allow things like that in proofs you end up with nonsense like 1 = 0 Multiplying 0 by infinity is the equivalent of 0 0 which is undefined
What is zero times infinity? - Mathematics Stack Exchange If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity? Do they cancel one another out and equal any number since any
Why is $\infty\times 0$ indeterminate? - Mathematics Stack Exchange In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form Your title says something else than "infinity times zero" It says "infinity to the zeroth power"