Why is this not 0 on 50g or Prime?

[Valentin Albillo]

(07-16-2018 03:35 PM)Joe Horn Wrote:  \[\frac { 1 }{ \infty +\cfrac { 1 }{ 0 } } =\frac { 1 }{ \infty +\infty } =\frac { 1 }{ \infty } =0\]The above is correct, no?

No.

Quote:Why then do both the HP 50g (in exact mode) and the HP Prime (in CAS view) say that the first expression, 1/(inf+1/0), is "undefined"?

Because it is. Mathematically, 1/0 is undefined, period,

Very, very informally you can see why this way:

The value of 1/0 depends on the sign of 0.

• In case of +0, 1/+0 would be +Inf and your denominator would be Inf + Inf = Inf. So far so good.
• In case of -0, 1/-0 would be -Inf and your denominator would be Inf - Inf = Undefined.

So, without knowing the sign of 0 the denominator is Undefined and the calculator is Ok.

Very informally. It can be made mora rigorous by taking limits, etc. but it would be overkill.

Regards.
V.
.