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In the mathematical notation for image and kernel one usually writes $\ker$ for kernel and $\DeclareMathOperator{\img}{Im}\img$ for image. Why is the "k" small but the "I" big?

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    $\begingroup$ I do not capitalize $\text{im}$. $\endgroup$ – Git Gud Mar 12 '15 at 22:13
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    $\begingroup$ I don't capitalize $\text{im}$ either. Some people capitalize $\text{Ker}$, even. It's a wild world out there. $\endgroup$ – Qiaochu Yuan Mar 12 '15 at 22:15
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    $\begingroup$ There is no uniform notation: both are capitalised in French. $\endgroup$ – Bernard Mar 12 '15 at 22:24
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    $\begingroup$ I don't capitalize either , since $Im$ can refer to an imaginary part $\endgroup$ – krirkrirk Mar 12 '15 at 22:26
  • $\begingroup$ ok great thanks for the comments. I will write both small then :) $\endgroup$ – Loreno Heer Mar 12 '15 at 22:49
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CW answer summing up comments, to push it from unanswered queue:

There is no uniform notation. It may or may not be capitalised.

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