What is the difference between the summations?

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What is the difference between the summation $$sum_{1 leq i<j leq n} f(i,j)$$ and $$sum_{1leq i} sum_{<j leq n} f(i,j)?$$

edited Nov 13 at 17:16

asked Nov 13 at 16:43

Of course it's not me

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Notation, I suppose. It's still the same sum.
– Sean Roberson
Nov 13 at 17:27

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What is the difference between the summation $$sum_{1 leq i<j leq n} f(i,j)$$ and $$sum_{1leq i} sum_{<j leq n} f(i,j)?$$

edited Nov 13 at 17:16

asked Nov 13 at 16:43

Of course it's not me

34414

1

Notation, I suppose. It's still the same sum.
– Sean Roberson
Nov 13 at 17:27

add a comment |

up vote
-1
down vote

favorite

What is the difference between the summation $$sum_{1 leq i<j leq n} f(i,j)$$ and $$sum_{1leq i} sum_{<j leq n} f(i,j)?$$

edited Nov 13 at 17:16

asked Nov 13 at 16:43

Of course it's not me

34414

What is the difference between the summation $$sum_{1 leq i<j leq n} f(i,j)$$ and $$sum_{1leq i} sum_{<j leq n} f(i,j)?$$

algebra-precalculus summation notation

edited Nov 13 at 17:16

asked Nov 13 at 16:43

Of course it's not me

34414

edited Nov 13 at 17:16

asked Nov 13 at 16:43

Of course it's not me

34414

edited Nov 13 at 17:16

asked Nov 13 at 16:43

Of course it's not me

34414

asked Nov 13 at 16:43

Of course it's not me

34414

asked Nov 13 at 16:43

Of course it's not me

34414

1

Notation, I suppose. It's still the same sum.
– Sean Roberson
Nov 13 at 17:27

add a comment |

1

Notation, I suppose. It's still the same sum.
– Sean Roberson
Nov 13 at 17:27

Notation, I suppose. It's still the same sum.
– Sean Roberson
Nov 13 at 17:27

add a comment |

2 Answers
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The second is ambiguous. $sum$ usually means you will iterate over some index individually. A double sum implies summing over two indices individually.

The first version you give implies summing with respect to $i,j$ in a single intration, whereas the second vaguely implies two.

So I'd say the first is the better of the two, the second having ambiguous meaning.

answered Nov 13 at 18:24

TurlocTheRed

59319

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The second one is nonsense; the condition in the sum, $<jleq n$, doesn't mean anything.

answered Nov 13 at 20:06

Deusovi

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
0
down vote

The second is ambiguous. $sum$ usually means you will iterate over some index individually. A double sum implies summing over two indices individually.

The first version you give implies summing with respect to $i,j$ in a single intration, whereas the second vaguely implies two.

So I'd say the first is the better of the two, the second having ambiguous meaning.

answered Nov 13 at 18:24

TurlocTheRed

59319

add a comment |

up vote
0
down vote

The second is ambiguous. $sum$ usually means you will iterate over some index individually. A double sum implies summing over two indices individually.

The first version you give implies summing with respect to $i,j$ in a single intration, whereas the second vaguely implies two.

So I'd say the first is the better of the two, the second having ambiguous meaning.

answered Nov 13 at 18:24

TurlocTheRed

59319

add a comment |

up vote
0
down vote

The second is ambiguous. $sum$ usually means you will iterate over some index individually. A double sum implies summing over two indices individually.

The first version you give implies summing with respect to $i,j$ in a single intration, whereas the second vaguely implies two.

So I'd say the first is the better of the two, the second having ambiguous meaning.

answered Nov 13 at 18:24

TurlocTheRed

59319

The second is ambiguous. $sum$ usually means you will iterate over some index individually. A double sum implies summing over two indices individually.

The first version you give implies summing with respect to $i,j$ in a single intration, whereas the second vaguely implies two.

So I'd say the first is the better of the two, the second having ambiguous meaning.

answered Nov 13 at 18:24

TurlocTheRed

59319

answered Nov 13 at 18:24

TurlocTheRed

59319

answered Nov 13 at 18:24

TurlocTheRed

59319

answered Nov 13 at 18:24

TurlocTheRed

59319

add a comment |

up vote
0
down vote

The second one is nonsense; the condition in the sum, $<jleq n$, doesn't mean anything.

answered Nov 13 at 20:06

Deusovi

2,1261920

add a comment |

up vote
0
down vote

The second one is nonsense; the condition in the sum, $<jleq n$, doesn't mean anything.

answered Nov 13 at 20:06

Deusovi

2,1261920

add a comment |

up vote
0
down vote

The second one is nonsense; the condition in the sum, $<jleq n$, doesn't mean anything.

answered Nov 13 at 20:06

Deusovi

2,1261920

The second one is nonsense; the condition in the sum, $<jleq n$, doesn't mean anything.

answered Nov 13 at 20:06

Deusovi

2,1261920

answered Nov 13 at 20:06

Deusovi

2,1261920

answered Nov 13 at 20:06

Deusovi

2,1261920

answered Nov 13 at 20:06

Deusovi

2,1261920

add a comment |

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