document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205268>Question 1205268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What number is in between -2 and -0.75\r<BR>\n" );
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document.write( "There are infinitely many numbers between -2 and -0.75, but one number we could pick on is the midpoint.\r<BR>\n" );
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document.write( "Add up the values and then divide in half\r<BR>\n" );
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document.write( "Add: -2+(-0.75) = -2-0.75 = -2.75<BR>\n" );
document.write( "Divide in half: -2.75/2 = <font color=red>-1.375</font><BR>\n" );
document.write( "The value <font color=red>-1.375</font> is between -2 and -0.75<BR>\n" );
document.write( "This is known as the arithmetic mean.\r<BR>\n" );
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document.write( "Or we could apply the geometric mean<BR>\n" );
document.write( "Multiply the values and then apply the square root.\r<BR>\n" );
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document.write( "Multiply: -2*(-0.75) = 1.5<BR>\n" );
document.write( "sqrt(1.5) = 1.2247 approximately<BR>\n" );
document.write( "Make the result negative so it's in between the two negative values<BR>\n" );
document.write( "<font color=red>-1.2247 approximately</font> is between -2 and -0.75\r<BR>\n" );
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document.write( "Edit: @ikleyn, fair enough, the geometric mean approach seemed a bit flimsy. However, we could treat it like finding the geometric mean of 2 and 0.75 and then make the result negative. \r<BR>\n" );
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document.write( "Another thing we could do is find the distance between the given values<BR>\n" );
document.write( "distance = |a-b| = |-2-(-0.75)| = |-2+0.75| = |-1.25| = 1.25<BR>\n" );
document.write( "Then cut this distance into N pieces, let's say N = 10<BR>\n" );
document.write( "1.25/N = 1.25/10 = 0.125\r<BR>\n" );
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document.write( "Let k be some integer on the interval 0 < k < N<BR>\n" );
document.write( "In this case 0 < k < 10\r<BR>\n" );
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document.write( "Then let's add some multiple of 0.125 to the left endpoint -2, to land somewhere between -2 and -0.75<BR>\n" );
document.write( "We're evaluating -2+0.125k for k = 1 through k = 9<BR>\n" );
document.write( "If k = 1, then -2 + 0.125k = -2 + 0.125*1 = <font color=red>-1.875</font><BR>\n" );
document.write( "If k = 2, then -2 + 0.125k = -2 + 0.125*2 = <font color=red>-1.75</font><BR>\n" );
document.write( "If k = 3, then -2 + 0.125k = -2 + 0.125*3 = <font color=red>-1.625</font><BR>\n" );
document.write( "If k = 4, then -2 + 0.125k = -2 + 0.125*4 = <font color=red>-1.5</font><BR>\n" );
document.write( "If k = 5, then -2 + 0.125k = -2 + 0.125*5 = <font color=red>-1.375</font><BR>\n" );
document.write( "If k = 6, then -2 + 0.125k = -2 + 0.125*6 = <font color=red>-1.25</font><BR>\n" );
document.write( "If k = 7, then -2 + 0.125k = -2 + 0.125*7 = <font color=red>-1.125</font><BR>\n" );
document.write( "If k = 8, then -2 + 0.125k = -2 + 0.125*8 = <font color=red>-1</font><BR>\n" );
document.write( "If k = 9, then -2 + 0.125k = -2 + 0.125*9 = <font color=red>-0.875</font><BR>\n" );
document.write( "Each of the results {<font color=red>-1.875</font>, <font color=red>-1.75</font>, <font color=red>-1.625</font>, <font color=red>-1.5</font>, <font color=red>-1.375</font>, <font color=red>-1.25</font>, <font color=red>-1.125</font>, <font color=red>-1</font>, <font color=red>-0.875</font>} are between -2 and -0.75\r<BR>\n" );
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document.write( "Notes: If k = 0, then -2+0.125k = -2 is the left endpoint, while k = 10 means -2+0.125k = -0.75 is the right endpoint.\r<BR>\n" );
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document.write( "There's nothing special about N = 10. We could have easily made N = 20 or whatever positive whole number you want.\r<BR>\n" );
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document.write( "And yet another approach is to select the number -1 since it's between -2 and -0.75, and then tack on some random string of decimal digits.<BR>\n" );
document.write( "Eg: <font color=red>-1.2345</font> or <font color=red>-1.6789</font><BR>\n" );
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