12/10/2022, 10:07 PM
Posts like this by James are really gold, I'd like to collect them and make some pdf, so that they will be saved by possible problems on the forum. There is alot to study here.
Right now I just can make a quick superficial comment: this makes me think of this conversation we had one year ago about the analogy sums:integral=omega notation:composition integral.
This makes me wonder if we can add the missing columns of the analogy
\(\displaystyle \sum / \int \,\sim\, \Omega / \int ...\bullet z\)
\(\Delta/ D \,\sim\, ?? / ??\)
\(n! / n! \,\sim\, ?? / ??\)
\(2^x / e^x \,\sim\, ?? / ??\)
\((x)_n / x^n \,\sim\, ??/??\)
\(Newton/ Taylor \, \sim \, ??/??\)
\(\Delta^n/ {\frac{d^z}{d^zx}} \,\sim\, ?? / ??\) fractional calculus?
Right now I just can make a quick superficial comment: this makes me think of this conversation we had one year ago about the analogy sums:integral=omega notation:composition integral.
This makes me wonder if we can add the missing columns of the analogy
\(\displaystyle \sum / \int \,\sim\, \Omega / \int ...\bullet z\)
\(\Delta/ D \,\sim\, ?? / ??\)
\(n! / n! \,\sim\, ?? / ??\)
\(2^x / e^x \,\sim\, ?? / ??\)
\((x)_n / x^n \,\sim\, ??/??\)
\(Newton/ Taylor \, \sim \, ??/??\)
\(\Delta^n/ {\frac{d^z}{d^zx}} \,\sim\, ?? / ??\) fractional calculus?
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
