Mixing
Regarding notations in one-sided limits that approach negative values
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This is something that's been giving me trouble to wrap my mind around. When observing values slightly to the left and to the right of said value (for calculating one-sided limits), if you've got a positive value, the notations are as follows, put in layman's terms:
$1^-$ is a number ever so slightly smaller than $1$(0,99999...) and $1^+$ is a number ever so slightly larger than $1$ (1,000...001)
Now, when we talk about negative values, is $-1^-$ a number slightly larger ($-0,999999...$) or slightly smaller ($-1,000...001$) than $-1$?
In other words, does $-1^-$ mean we are approaching $-1$ from the left or the right?
limits elementary-number-theory real-numbers
asked Jan 27 at 16:22
ArcturusArcturus
1217
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add a comment |
$begingroup$
This is something that's been giving me trouble to wrap my mind around. When observing values slightly to the left and to the right of said value (for calculating one-sided limits), if you've got a positive value, the notations are as follows, put in layman's terms:
$1^-$ is a number ever so slightly smaller than $1$(0,99999...) and $1^+$ is a number ever so slightly larger than $1$ (1,000...001)
Now, when we talk about negative values, is $-1^-$ a number slightly larger ($-0,999999...$) or slightly smaller ($-1,000...001$) than $-1$?
In other words, does $-1^-$ mean we are approaching $-1$ from the left or the right?
limits elementary-number-theory real-numbers
asked Jan 27 at 16:22
ArcturusArcturus
1217
$endgroup$
2
$begingroup$
- means always from the left, + means always from the right, independently on the value of the point, negative, positive, zero...
$endgroup$
– Roman Hric
Jan 27 at 16:35
add a comment |
$begingroup$
This is something that's been giving me trouble to wrap my mind around. When observing values slightly to the left and to the right of said value (for calculating one-sided limits), if you've got a positive value, the notations are as follows, put in layman's terms:
$1^-$ is a number ever so slightly smaller than $1$(0,99999...) and $1^+$ is a number ever so slightly larger than $1$ (1,000...001)
Now, when we talk about negative values, is $-1^-$ a number slightly larger ($-0,999999...$) or slightly smaller ($-1,000...001$) than $-1$?
In other words, does $-1^-$ mean we are approaching $-1$ from the left or the right?
limits elementary-number-theory real-numbers
asked Jan 27 at 16:22
ArcturusArcturus
1217
$endgroup$
This is something that's been giving me trouble to wrap my mind around. When observing values slightly to the left and to the right of said value (for calculating one-sided limits), if you've got a positive value, the notations are as follows, put in layman's terms:
$1^-$ is a number ever so slightly smaller than $1$(0,99999...) and $1^+$ is a number ever so slightly larger than $1$ (1,000...001)
Now, when we talk about negative values, is $-1^-$ a number slightly larger ($-0,999999...$) or slightly smaller ($-1,000...001$) than $-1$?
In other words, does $-1^-$ mean we are approaching $-1$ from the left or the right?
limits elementary-number-theory real-numbers
limits elementary-number-theory real-numbers
asked Jan 27 at 16:22
ArcturusArcturus
1217
asked Jan 27 at 16:22
ArcturusArcturus
1217
asked Jan 27 at 16:22
ArcturusArcturus
1217
asked Jan 27 at 16:22
ArcturusArcturus
1217
asked Jan 27 at 16:22
ArcturusArcturus
1217
1217
2
$begingroup$
- means always from the left, + means always from the right, independently on the value of the point, negative, positive, zero...
$endgroup$
– Roman Hric
Jan 27 at 16:35
add a comment |
2
$begingroup$
- means always from the left, + means always from the right, independently on the value of the point, negative, positive, zero...
$endgroup$
– Roman Hric
Jan 27 at 16:35
2
2
$begingroup$
- means always from the left, + means always from the right, independently on the value of the point, negative, positive, zero...
$endgroup$
– Roman Hric
Jan 27 at 16:35
$begingroup$
- means always from the left, + means always from the right, independently on the value of the point, negative, positive, zero...
$endgroup$
– Roman Hric
Jan 27 at 16:35
add a comment |
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$begingroup$
- means always from the left, + means always from the right, independently on the value of the point, negative, positive, zero...
$endgroup$
– Roman Hric
Jan 27 at 16:35