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(Section 2.7: Precise Definitions of Limits)
2.7.3
Where Do We Look For Winners?
We only care about players that are “close” to
x
=
a
(here,
x
=
4
).
We ignore
a
itself, and we say in this context that
a
is not “close” to itself.
In particular, we only care about players that are strictly between 0 and
±
units of
a
, where
>
0
. Like
, the Greek letter
(“delta”) often represents
a small positive quantity. Here, we can think of
as the halfwidth of a
“symmetric punctured interval” that is symmetric about
x
=
a
, though we
delete
a
itself as a “puncture.”
Symbolically:
Player
x
is "close" to
a
±
a
²
³
<
x
<
a
+
x
´
a
()
Subtract
a
from all three parts.
±
²
<
x
²
a
<
x
´
a
±
0
<
x
²
a
<
This makes sense, because
x
±
a
represents the distance between Player
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 sturst
 Limits

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