I am just a hobby mathematician, but it seems to me like this: 1^oo := lim(1^n) = lim(1) = 1.
The other 'limits' seem to me to be an inadmissible 'exchange' of limits: 1 != (1 + 1/n) for any finite n On Sat 6. Nov 2021 at 14:15, Oscar Benjamin <[email protected]> wrote: > On Sat, 6 Nov 2021 at 11:58, Anderson Bhat <[email protected]> > wrote: > > > > Hello guys , I am working on couple of Pr's extending the functionality > of the doit method in the concrete module , I noticed that one > inconsistency leads to couple of errors . Product(1, (n, 1, oo)).doit() > returns 1 and 1**oo returns NaN. Other integers work as expected . These > expressions are equivalent right ??? or am I missing something ! > > The expression 1**oo is indeterminate because there are different ways > that you could arrive at this form that have different limits: > > In [31]: limit((1 + 1/n)**n, n, oo) > Out[31]: ℯ > > In [32]: limit((1 + 1/n**2)**n, n, oo) > Out[32]: 1 > > In [33]: limit((1 + 1/sqrt(n))**n, n, oo) > Out[33]: ∞ > > The product in your case defines a particular limit so it is not > indeterminate: > > In [38]: Product(1, (n, 1, m)).doit() > Out[38]: 1 > > In [39]: limit(Product(1, (n, 1, m)).doit(), m, oo) > Out[39]: 1 > > -- > Oscar > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxTS%2BA32brrRS7xZ7Rr7kJ%2BLG%2BxJ6Jre1sys8_iHVzZ7tg%40mail.gmail.com > . > -- Best regards, Peter Stahlecker -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CABKqA0Z0%2B%3DFCuTTG9o3NqzHWf89YBDdmP1upWtsNcBgyWxxLPA%40mail.gmail.com.
