even number

Error message

User error: Socket error: Could not connect to "http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03F03+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D" (proxy: 0): Connection refused in ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03F03+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: Socket error: Could not connect to "http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03C05+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D" (proxy: 0): Connection refused in ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03C05+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: Socket error: Could not connect to "http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03B22+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D" (proxy: 0): Connection refused in ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03B22+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: Socket error: Could not connect to "http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03B05+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D" (proxy: 0): Connection refused in ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "getFormat" via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).
User error: missing stream in "readStream" http://planetmath.org:8890/sparql?query=%0APREFIX+msc%3A+%3Chttp%3A%2F%2Fmsc2010.org%2Fresources%2FMSC%2F2010%2F%3E+PREFIX+skos%3A+%3Chttp%3A%2F%2Fwww.w3.org%2F2004%2F02%2Fskos%2Fcore%23%3E+PREFIX+dct%3A+%3Chttp%3A%2F%2Fpurl.org%2Fdc%2Fterms%2F%3E+PREFIX+local%3A+%3Chttp%3A%2F%2Flocal.virt%2F%3E+SELECT+%3Flabel+WHERE+%7B+GRAPH+%3Chttp%3A%2F%2Flocalhost%3A8890%2FDAV%2Fhome%2Fpm%2Frdf_sink%23this%3E+%7B+msc%3A03B05+skos%3AprefLabel+%3Flabel+FILTER+langMatches%28+lang%28%3Flabel%29%2C+%22en%22+%29+%7D%7D via ARC2_Reader in _sparql_request() (line 92 of /home/jcorneli/beta/sites/all/modules/sparql/sparql.module).

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even number

Definition Suppose $k$ is an integer. If there exists an integer $r$ such that $k=2r+1$ , then $k$ is an odd number. If there exists an integer $r$ such that $k=2r$ , then $k$ is an even number.

The concept of even and odd numbers are most easily understood in the binary base. Then the above definition simply states that even numbers end with a $0$ , and odd numbers end with a $1$ .

0.0.1 Properties

1.

Every integer is either even or odd. This can be proven using induction, or using the fundamental theorem of arithmetic.
2.

An integer $k$ is even (odd) if and only if $k^{2}$ is even (odd).

Defines:

odd number, even integer, odd integer, even, odd

Type of Math Object:

Definition

Major Section:

Reference

Mathematics Subject Classification

11-00 no label found03-00 no label found

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