Have you got their number ?

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1 total messages Started by Kali Sat, 09 Oct 1999 00:00

#80

Author: Kali
Date: Sat, 09 Oct 1999 00:00

67 lines
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I have posted the folowing problem there:

All sets, X(A, R) below are real-valued functions with domain A.

What are the cardinal numbers of:

K(R, R)    the set of all real-valued constant functions over R.
D(R, R)  the set of all real-valued differentiable functions over R.
C(Q, R)    the set of all real-valued continuous functions over Q.
C(R, R)    the set of all real-valued continuous functions over R.
F(R, R)    the set of all real-valued functions over R.

Kali


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http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2314.1000" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#a6caf0>
<DIV>
<DIV>I have posted the folowing problem there:</DIV>
<DIV>&nbsp;</DIV>
<DIV>All sets, X(A, R) below are real-valued functions with =
domain&nbsp;A.</DIV>
<DIV>&nbsp;</DIV>
<DIV>What are the cardinal numbers of:</DIV>
<DIV>&nbsp;</DIV>
<DIV>K(R, R) &nbsp;&nbsp; the set of all real-valued constant functions =
over=20
R.</DIV>
<DIV>D(R, R)&nbsp; the set of all real-valued =
differentiable&nbsp;functions over=20
R.</DIV>
<DIV>
<DIV>
<DIV>
<DIV>C(<FONT color=3D#800080>Q, </FONT>R)&nbsp;&nbsp;&nbsp; the set of =
all=20
real-valued continuous functions over <FONT =
color=3D#800080>Q.</FONT></DIV>
<DIV>C(R, R) &nbsp;&nbsp; the set of all real-valued =
continuous&nbsp;functions=20
over R.</DIV>
<DIV>F(R, R)&nbsp;&nbsp;&nbsp; the set of all real-valued functions over =

R.</DIV>
<DIV>&nbsp;</DIV>
<DIV>Kali</DIV>
<DIV>&nbsp;</DIV></DIV></DIV></DIV></DIV></BODY></HTML>

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