What exactly is infinity? - Mathematics Stack Exchange The infinite manifold of two or three dimensions, the mathematical beings which depend on a number of variables greater even than three, any number in fact, still have no greater power than the linear continuum
How can Cyclic groups be infinite - Mathematics Stack Exchange I am a little confused about how a cyclic group can be infinite To provide an example, look at $\\langle 1\\rangle$ under the binary operation of addition You can never make any negative numbers with
sequences and series - What is the sum of an infinite resistor ladder . . . Here's a proof by induction that the resistance of a finite version of this ladder with $\ n\ $ rungs is indeed homogeneous of degree $1$ in the variable $\ R\ $ Taking the limit as $\ n\rightarrow\infty\ $ (assuming it exists $\left \right ^\color {red} {\dagger}$) then shows that the resistance of the infinite ladder depicted in Figure $2
I have learned that 1 0 is infinity, why isnt it minus infinity? An infinite number? Kind of, because I can keep going around infinitely However, I never actually give away that sweet This is why people say that 1 0 "tends to" infinity - we can't really use infinity as a number, we can only imagine what we are getting closer to as we move in the direction of infinity
Can an infinite sum of irrational numbers be rational? An infinite sum of irrational numbers can be rational PROOF: Let the set A be all the positive irrational numbers and the set B be the negative irrational numbers