Mixing
Understanding the meaning of the notation $([x_{i-1},x_i],t_i)$
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When learning about tagged partitions I'm introduced to the notation $([x_{i-1},x_i],t_i)$. Is this referring to all numbers y such that $x_{i-1}<y<t_i$ ? Or does it mean something else? Cheers
notation
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
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add a comment |
$begingroup$
When learning about tagged partitions I'm introduced to the notation $([x_{i-1},x_i],t_i)$. Is this referring to all numbers y such that $x_{i-1}<y<t_i$ ? Or does it mean something else? Cheers
notation
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
$endgroup$
1
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Some more context might be helpful here, but I suspect that you're studying Riemann sums, and in this context, $[x_{i-1}, x_i]$ is one of the intervals in your partition, and $t_i$ is a point in this interval at which the function is sampled. So, if you were to form a Riemann sum over a tagged partition containing this pair, then one of the sum terms would be $f(t_i) cdot (x_i - x_{i-1})$.
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– Theo Bendit
Jan 10 at 4:33
2
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It is literally an ordered pair, where the first coordinate is the interval $[x_{i-1},x_i]$ and the second coordinate is the number $t_i$.
$endgroup$
– Cheerful Parsnip
Jan 10 at 4:51
add a comment |
$begingroup$
When learning about tagged partitions I'm introduced to the notation $([x_{i-1},x_i],t_i)$. Is this referring to all numbers y such that $x_{i-1}<y<t_i$ ? Or does it mean something else? Cheers
notation
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
$endgroup$
When learning about tagged partitions I'm introduced to the notation $([x_{i-1},x_i],t_i)$. Is this referring to all numbers y such that $x_{i-1}<y<t_i$ ? Or does it mean something else? Cheers
notation
notation
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
asked Jan 10 at 4:25
Henry MullenHenry Mullen
162
162
1
$begingroup$
Some more context might be helpful here, but I suspect that you're studying Riemann sums, and in this context, $[x_{i-1}, x_i]$ is one of the intervals in your partition, and $t_i$ is a point in this interval at which the function is sampled. So, if you were to form a Riemann sum over a tagged partition containing this pair, then one of the sum terms would be $f(t_i) cdot (x_i - x_{i-1})$.
$endgroup$
– Theo Bendit
Jan 10 at 4:33
2
$begingroup$
It is literally an ordered pair, where the first coordinate is the interval $[x_{i-1},x_i]$ and the second coordinate is the number $t_i$.
$endgroup$
– Cheerful Parsnip
Jan 10 at 4:51
add a comment |
1
$begingroup$
Some more context might be helpful here, but I suspect that you're studying Riemann sums, and in this context, $[x_{i-1}, x_i]$ is one of the intervals in your partition, and $t_i$ is a point in this interval at which the function is sampled. So, if you were to form a Riemann sum over a tagged partition containing this pair, then one of the sum terms would be $f(t_i) cdot (x_i - x_{i-1})$.
$endgroup$
– Theo Bendit
Jan 10 at 4:33
2
$begingroup$
It is literally an ordered pair, where the first coordinate is the interval $[x_{i-1},x_i]$ and the second coordinate is the number $t_i$.
$endgroup$
– Cheerful Parsnip
Jan 10 at 4:51
1
1
$begingroup$
Some more context might be helpful here, but I suspect that you're studying Riemann sums, and in this context, $[x_{i-1}, x_i]$ is one of the intervals in your partition, and $t_i$ is a point in this interval at which the function is sampled. So, if you were to form a Riemann sum over a tagged partition containing this pair, then one of the sum terms would be $f(t_i) cdot (x_i - x_{i-1})$.
$endgroup$
– Theo Bendit
Jan 10 at 4:33
$begingroup$
Some more context might be helpful here, but I suspect that you're studying Riemann sums, and in this context, $[x_{i-1}, x_i]$ is one of the intervals in your partition, and $t_i$ is a point in this interval at which the function is sampled. So, if you were to form a Riemann sum over a tagged partition containing this pair, then one of the sum terms would be $f(t_i) cdot (x_i - x_{i-1})$.
$endgroup$
– Theo Bendit
Jan 10 at 4:33
2
2
$begingroup$
It is literally an ordered pair, where the first coordinate is the interval $[x_{i-1},x_i]$ and the second coordinate is the number $t_i$.
$endgroup$
– Cheerful Parsnip
Jan 10 at 4:51
$begingroup$
It is literally an ordered pair, where the first coordinate is the interval $[x_{i-1},x_i]$ and the second coordinate is the number $t_i$.
$endgroup$
– Cheerful Parsnip
Jan 10 at 4:51
add a comment |
1 Answer
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If $P={x_0,x_1,...,x_n}$ is a partition of the intervall $[a,b]$, then put $I_i:=[x_{i-1},x_i], quad (i=1,...,n) $.
Then $([x_{i-1},x_i],t_i)$ means that $t_i in I_i.$
answered Jan 10 at 5:52
FredFred
45.6k1848
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1 Answer
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$begingroup$
If $P={x_0,x_1,...,x_n}$ is a partition of the intervall $[a,b]$, then put $I_i:=[x_{i-1},x_i], quad (i=1,...,n) $.
Then $([x_{i-1},x_i],t_i)$ means that $t_i in I_i.$
answered Jan 10 at 5:52
FredFred
45.6k1848
$endgroup$
add a comment |
$begingroup$
If $P={x_0,x_1,...,x_n}$ is a partition of the intervall $[a,b]$, then put $I_i:=[x_{i-1},x_i], quad (i=1,...,n) $.
Then $([x_{i-1},x_i],t_i)$ means that $t_i in I_i.$
answered Jan 10 at 5:52
FredFred
45.6k1848
$endgroup$
add a comment |
$begingroup$
If $P={x_0,x_1,...,x_n}$ is a partition of the intervall $[a,b]$, then put $I_i:=[x_{i-1},x_i], quad (i=1,...,n) $.
Then $([x_{i-1},x_i],t_i)$ means that $t_i in I_i.$
answered Jan 10 at 5:52
FredFred
45.6k1848
$endgroup$
If $P={x_0,x_1,...,x_n}$ is a partition of the intervall $[a,b]$, then put $I_i:=[x_{i-1},x_i], quad (i=1,...,n) $.
Then $([x_{i-1},x_i],t_i)$ means that $t_i in I_i.$
answered Jan 10 at 5:52
FredFred
45.6k1848
answered Jan 10 at 5:52
FredFred
45.6k1848
answered Jan 10 at 5:52
FredFred
45.6k1848
answered Jan 10 at 5:52
FredFred
45.6k1848
45.6k1848
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add a comment |
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1
$begingroup$
Some more context might be helpful here, but I suspect that you're studying Riemann sums, and in this context, $[x_{i-1}, x_i]$ is one of the intervals in your partition, and $t_i$ is a point in this interval at which the function is sampled. So, if you were to form a Riemann sum over a tagged partition containing this pair, then one of the sum terms would be $f(t_i) cdot (x_i - x_{i-1})$.
$endgroup$
– Theo Bendit
Jan 10 at 4:33
2
$begingroup$
It is literally an ordered pair, where the first coordinate is the interval $[x_{i-1},x_i]$ and the second coordinate is the number $t_i$.
$endgroup$
– Cheerful Parsnip
Jan 10 at 4:51