Problems with Zero - Numberphile

What people said

Recommends Xoque55 · 2013-10 · Mathematics Stack Exchange · on “Value of tan(pi/2)”

Instead of trying to "evaluate" $\tan(\pi/2)$ by simply observing its graph, why not go back to good old-fashioned trig arguments? If you were to evaluate the value of $\tan(\pi/2)$ on the unit circle, you would essentially be constructing this argument: $$ \tan(\pi/2) = \frac{\sin(\pi/2)}{\cos(\pi/2)} = \frac{1}{0} $$ Note that is the same as asking for the $y$-coordinate of the point (0,1) on the unit circle to be divided by its $x$-coordinate. Due to various reasons (see [LINK] ; or Numberphile's wonderfully informative video Problems with Zero [this video] ), mathematicians have not defined what it means to divide by zero because the value is not consistent in various contexts. So division by

Recommends Josh · 2014-07 · Mathematics Stack Exchange · on “Division by zero”

Lots of great answers here. Numberphile also has an interesting video where they discuss some of the issues with division by 0. [this video]

Recommends Evan Teran · 2015-12 · Stack Overflow · on “Why does division by zero in IEEE754 standard results in Infinite value?”

Just to add, Numberphile ( [this video] ) has a great video on why `x / 0` should not be considered infinity including addressing the thought that "I can take 0 from x an infinite number of times". The summary is that form a algebra point of view, you are are never supposed to say something is "equal to infinity", since at you point out it's not a number.

Recommends Brevan Ellefsen · 2016-03 · Mathematics Stack Exchange · on “Why limits of functions which are not $\frac{0}{0}$ have an asymptote”

@ErfanAhmadi the short reason is that, for any integer $n$ other than $0$, $\frac n0 = \pm \infty$, while you can basically make $\frac 00$ equal anything you want.... The limit is different in every direction. Formally understanding two-sided limits is a calculus 3 topic, but this is a good layman video on the topic: [this video]

Recommends Christopher · 2018-06 · Stack Overflow · on “Divide by 0 error C#”

Division by 0 is not defined in mathemathics. In case you wonder why, this video can explain it better then me: [this video] And the computer is not able to calculate what Math Science has not figured out. Aside from that, there is also an issue with the types. You are division in integer, then cast to a type with decimal places. Either pick double/float to being with and live with the issues inherent in them: [LINK] Or accept that imprecision in dividing with Integers. Also you define "value" but never use it.

Recommends Evert · 2020-12 · Stack Overflow · on “Why it throws "Floating Point Exception" if I divide a floating number by zero?”

Dividing by 0 does not necessarily result in infinity. There's a good numberphile [this video] video that goes into this. More importantly here, the IEEE 754 floating point standard (which is what most languages/cpus use) dictates that dividing by 0 should result in NaN, and many programming languages just turn this into an error. This is not linux specific. I don't even think Linux itself can raise something called an exception, so this must be a higher-level language thing.

Recommends PrincessEev · 2023-08 · Mathematics Stack Exchange · on “Is the equation $\sec (\pi/2)$= $\tan (\pi/2)$ true?”

"While both sec(π/2) and tan(π/2) are undefined they are both basically 1/0." - You could just make as convincing a case that they're $-1/0$. This Numberphile video covers some related issues -- [this video]

Cites hasExams · 2013-01 · Mathematics Stack Exchange · on “how to show that $\lim_{z \to 0}z^z$ does not exist?”

What makes $0^0$ indeterminate? Here is a video by numberphile [this video] that claims that $z^z$ does not exist as $z \to 0$ where $z \in \mathbb C $ . I tried $$\lim_{x \to 0}(x+ix)^{(x+ix)}$$ and replaced $x$ by $-x$ and couple of tricks Limit[(x + I x^2)^(x + I x^2), x -> 0] in Mathematica, but I got $1$ . Did I misunderstand what is tried to be shown on that video?

Cites Jared Norman · 2014-05 · Mathematics Stack Exchange · on “Coefficients in a binomial expression”

Perhaps you should start with a simpler problem. Pascals triangle is 1,121,1331,etc... you can find it here [LINK] , but make sure you see how the next row is calculated from the previous. Lets look at 121. What is this saying in terms of polynomials? It is on the 2nd level so it tells you it can simplify a polynomial of the form $(ax+b)^2$ for some numbers $a$ and $b$. If you are asked to simplify $(3x-2)^2$ then $a=3, b=-2$. For example, $$(ax+b)^2 = 1(ax)^2(b)^0 + 2(ax)^1(b)^1 + 1(ax)^0(b)^2$$ Do you see how the 1,2,1 were used? And how the $ax$ and $b$ were combined? Remember that anything to the power $0$ is $1$ (well, except $0$, but that's sort of an edge case [this video] ) Lets do a poly

Cites Secret · 2014-11 · Mathematics Stack Exchange · on “0 to the power of 0, what does the essential discontinuity actually look like?”

So having watch this clip by Numberphile which explains why $0^0$ is undefined [this video] And also this Link [LINK] And also this Zero to the zero power – is $0^0=1$? [LINK] I understand how when given a function of the form $x^y$ then you have the following results $$\lim_{x\rightarrow 0} x^0=1,$$ $$\lim_{y\rightarrow 0^+} 0^y=0,$$ and both the video and the mathforum link (and numerous others) mentioned about how when approaching form different directions you get different answers However, both google and mathematica failed to actually show what the discontinuity look like While a similar problematic case of " $\frac{0}{0}$ " indeterminate form gives rather consistently the shape of the essen