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Is there any definition of the sum of $n$ summands, when $n$ is not a natural number?
Clash Royale CLAN TAG#URR8PPP
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I think, from the algebraic point of view, that this doesn't make sense, since the addition of $n$ terms is defined "inductively" from the binary operation of the addition. This even yields the formula of $nx = x + x + cdots + x$, where the $x$ is added $n$ times (which I saw as a different operation than the multiplication in a ring, but an action of the natural numbers in the ring).
However, it would make sense to make a definition of adding $n in mathbbRsetminusmathbbN$ terms or summands? Something like the sense of a fractional derivative?
calculus fractional-iteration
asked Jul 24 at 4:36
Manuel Sánchez
84
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up vote
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I think, from the algebraic point of view, that this doesn't make sense, since the addition of $n$ terms is defined "inductively" from the binary operation of the addition. This even yields the formula of $nx = x + x + cdots + x$, where the $x$ is added $n$ times (which I saw as a different operation than the multiplication in a ring, but an action of the natural numbers in the ring).
However, it would make sense to make a definition of adding $n in mathbbRsetminusmathbbN$ terms or summands? Something like the sense of a fractional derivative?
calculus fractional-iteration
asked Jul 24 at 4:36
Manuel Sánchez
84
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I think, from the algebraic point of view, that this doesn't make sense, since the addition of $n$ terms is defined "inductively" from the binary operation of the addition. This even yields the formula of $nx = x + x + cdots + x$, where the $x$ is added $n$ times (which I saw as a different operation than the multiplication in a ring, but an action of the natural numbers in the ring).
However, it would make sense to make a definition of adding $n in mathbbRsetminusmathbbN$ terms or summands? Something like the sense of a fractional derivative?
calculus fractional-iteration
asked Jul 24 at 4:36
Manuel Sánchez
84
I think, from the algebraic point of view, that this doesn't make sense, since the addition of $n$ terms is defined "inductively" from the binary operation of the addition. This even yields the formula of $nx = x + x + cdots + x$, where the $x$ is added $n$ times (which I saw as a different operation than the multiplication in a ring, but an action of the natural numbers in the ring).
However, it would make sense to make a definition of adding $n in mathbbRsetminusmathbbN$ terms or summands? Something like the sense of a fractional derivative?
calculus fractional-iteration
asked Jul 24 at 4:36
Manuel Sánchez
84
edited Jul 24 at 11:49
asked Jul 24 at 4:36
Manuel Sánchez
84
asked Jul 24 at 4:36
Manuel Sánchez
84
asked Jul 24 at 4:36
Manuel Sánchez
84
84
add a comment |Â
add a comment |Â
1 Answer
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Markus Muller and Dierk Schleicher say there is.
http://www.mpmueller.net/HowToAdd.pdf
answered Jul 24 at 4:49
Steve B
34126
I love that people took the time to make sense of something so seemingly nonsensical!
– Sambo
Jul 24 at 16:52
Amazing. It's surprising that there's not many articles about those kind of definitions. Another article I found (same authors) can be found here: arxiv.org/abs/math/0502109
– Manuel Sánchez
Jul 31 at 5:06
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Markus Muller and Dierk Schleicher say there is.
http://www.mpmueller.net/HowToAdd.pdf
answered Jul 24 at 4:49
Steve B
34126
I love that people took the time to make sense of something so seemingly nonsensical!
– Sambo
Jul 24 at 16:52
Amazing. It's surprising that there's not many articles about those kind of definitions. Another article I found (same authors) can be found here: arxiv.org/abs/math/0502109
– Manuel Sánchez
Jul 31 at 5:06
add a comment |Â
up vote
3
down vote
accepted
Markus Muller and Dierk Schleicher say there is.
http://www.mpmueller.net/HowToAdd.pdf
answered Jul 24 at 4:49
Steve B
34126
I love that people took the time to make sense of something so seemingly nonsensical!
– Sambo
Jul 24 at 16:52
Amazing. It's surprising that there's not many articles about those kind of definitions. Another article I found (same authors) can be found here: arxiv.org/abs/math/0502109
– Manuel Sánchez
Jul 31 at 5:06
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Markus Muller and Dierk Schleicher say there is.
http://www.mpmueller.net/HowToAdd.pdf
answered Jul 24 at 4:49
Steve B
34126
Markus Muller and Dierk Schleicher say there is.
http://www.mpmueller.net/HowToAdd.pdf
answered Jul 24 at 4:49
Steve B
34126
answered Jul 24 at 4:49
Steve B
34126
answered Jul 24 at 4:49
Steve B
34126
answered Jul 24 at 4:49
Steve B
34126
34126
I love that people took the time to make sense of something so seemingly nonsensical!
– Sambo
Jul 24 at 16:52
Amazing. It's surprising that there's not many articles about those kind of definitions. Another article I found (same authors) can be found here: arxiv.org/abs/math/0502109
– Manuel Sánchez
Jul 31 at 5:06
add a comment |Â
I love that people took the time to make sense of something so seemingly nonsensical!
– Sambo
Jul 24 at 16:52
Amazing. It's surprising that there's not many articles about those kind of definitions. Another article I found (same authors) can be found here: arxiv.org/abs/math/0502109
– Manuel Sánchez
Jul 31 at 5:06
I love that people took the time to make sense of something so seemingly nonsensical!
– Sambo
Jul 24 at 16:52
I love that people took the time to make sense of something so seemingly nonsensical!
– Sambo
Jul 24 at 16:52
Amazing. It's surprising that there's not many articles about those kind of definitions. Another article I found (same authors) can be found here: arxiv.org/abs/math/0502109
– Manuel Sánchez
Jul 31 at 5:06
Amazing. It's surprising that there's not many articles about those kind of definitions. Another article I found (same authors) can be found here: arxiv.org/abs/math/0502109
– Manuel Sánchez
Jul 31 at 5:06
add a comment |Â
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