Infinity symbol

Infinity (like most symbols in math) has many different meanings, depending on context. If you look up the definition of "limit at infinity" or "limit is equal to infinity" in a real-analysis textbook, you'll usually see that it is treated differently from 'regular' limits, since that ∞ isn't actually a real-number. For example, you might see something like the following as the definition of a limit: The notation L = lim f(x) as x goes to c means that for any ε, there exists a δ such that for all u where |u - x| < δ, |f(u) - L| < ε. This definition gives meaning to things like "1 = lim sin(x) / x as x goes to 0". However, it doesn't give meaning to the notion "0 = lim 1/x as x goes to ∞", nor "∞ = lim 1/x2 as x goes to 0", since conditions like |f(u) - ∞| < ε or |∞ - x| < δ are not well-defined. Instead, you'll also see some additional definitions: The notation ∞ = lim f(x) as x goes to c means that for any N, there exists a δ such that for all u where |u - x| < δ, f(u) > N. The notation L = lim f(x) as x goes to ∞ means that for any ε, there exist a N such that for all u where u > N, |f(u) - L| < ε Sometimes these multiple definitions can be unified using, for example, the extended real numbers . This saves some writing by generalizing the |a - b| < c notion of "distance" to also work on ±∞. However, this is basically just a notational convenience -- you have to be wary of using the extended-real-numbers, because most of the properties that you take for granted of real numbers don't necessarily apply to the extended reals. For example, if you have real numbers obeying x = y + c, you also know that x - c = y. However, if any of these can be "±∞", the first equation doesn't necessarily make the second one true (For example, ∞ = 1 + ∞ is true when those symbols indicate operations on extended real numbers, but ∞ - ∞ = 1 is not true). Infinity has many other uses in mathematics, beyond limits, but it's where you'll probably come across it first. More involved uses of infinities have to distinguish between different kinds of infinities (such as with cardinalities and ordinalities) -- but that's a topic for another day. More on reddit.com

\item Obtain the one-to-one function $f_1$ and $f_2$ by cutting the graph of $f$ at a certain point ($x_1$, $y_1$) so that domain of ($f_1$)=($-∞$ , $x_1$] and domain ($f_2$)=[$x_1$,$... More on tex.stackexchange.com

A weird looking X or N? Are you talking about aleph? Though it's not really infinity to the power of infinity... More on reddit.com

Hi there, Can anyone tell me if there is a mathematical symbol for beyond? I’m thinking possibly “>” could work? I’m trying to say the phrase “to infinity and beyond” I have this: 2 [infinity symbol] & > Thanks! More on freemathhelp.com