| 2 | "Usually defined" since one need not necessarily implement functions as collections of ordered pairs. | ||
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A function $f:\Bbb R\rightarrow\Bbb R$ can be seen as a (certain) subset of $\Bbb R^2$ (Note: in fact the functions are usually defined to be certain subsets, but you can ignore this now) Two functions are the same when the corresponding subsets are the same. The names you choose for the coordinates in $f:\Bbb R\rightarrow\Bbb R$ are irrelevant. A function $f:\Bbb R\rightarrow\Bbb R$ can be seen as a (certain) subset of $\Bbb R^2$ (Note: in fact the functions are defined to be certain subsets, but you can ignore this now) Two functions are the same when the corresponding subsets are the same. The names you choose for the coordinates in $f:\Bbb R\rightarrow\Bbb R$ are irrelevant. A function $f:\Bbb R\rightarrow\Bbb R$ can be seen as a (certain) subset of $\Bbb R^2$ (Note: in fact the functions are usually defined to be certain subsets, but you can ignore this now) Two functions are the same when the corresponding subsets are the same. The names you choose for the coordinates in $f:\Bbb R\rightarrow\Bbb R$ are irrelevant. |
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| 1 | |||
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A function $f:\Bbb R\rightarrow\Bbb R$ can be seen as a (certain) subset of $\Bbb R^2$ (Note: in fact the functions are defined to be certain subsets, but you can ignore this now) Two functions are the same when the corresponding subsets are the same. The names you choose for the coordinates in $f:\Bbb R\rightarrow\Bbb R$ are irrelevant. |
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