Arg(z) arg (z) is not continuous since it has jumps of 2π 2 π. To find examples and explanations on the internet at the elementary calculus level, try googling the phrase continuous extension (or variations of it, such as extension by continuity) simultaneously with the phrase ap calculus. Following is the formula to calculate continuous compounding a = p e^(rt) continuous compound interest formula where, p = principal amount (initial investment) r = annual interest rate (as a · let z = x + iy z = x + i y be any complex number, then in general the argument of z z, i. e. Im interested in a continuous determination of the argument. I came up with the following definition of the argument which should make it continuous: · in fact, it turns out that every continuous function from a path connected space to $\mathbb r$ is a quotient map note that the closed map lemma cannot be generalised, for example $ (0,1)\to [0,1]$ is not closed. I know that the image of a continuous function is bounded, but im having trouble when it comes to prove this for vectorial functions. · closure of continuous image of closure ask question asked 12 years, modified 12 years, · of course having two variables introduces a few more details, but they are straightforward once you understand the idea. One thing to note is that tao is only talking about continuity on $ [0, \infty]$. The reason for using ap calculus instead of just calculus is to ensure that advanced stuff is filtered out. · 6 every metric is continuous means that a metric $d$ on a space $x$ is a continuous function in the topology on the product $x \times x$ determined by $d$. If you consider negatives, then multiplication ceases to be continuous from below at $\langle 0, \infty \rangle$ either. Proving the inverse of a continuous function is also continuous ask question asked 11 years, modified 7 years, If somebody could help me with a step-to-step proof, that would be great. · to understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function thats continuous on $\mathbb r$ but not uniformly continuous on $\mathbb r$.
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Arg(z) arg (z) is not continuous since it has jumps of 2π 2 π. To find examples and explanations on the internet at the elementary...
