document.write( "Question 1141176: I just watched a video with the following explanation:
\n" ); document.write( "To Show that a set is countable:
\n" ); document.write( "• Formally, we have to show that there exists a bijective function between the set in question and the set of natural numbers.
\n" ); document.write( "• Informally, we have to show to the elements of the set can be put in an order, so that:
\n" ); document.write( "o No element will ever be repeated.
\n" ); document.write( "o And no element will ever be missed out. \r
\n" ); document.write( "\n" ); document.write( "I then watched another video that said that such are \"one-to-One\" and that such should be able to pass the \"horizontal line test.\"\r
\n" ); document.write( "\n" ); document.write( "But X as 1,2,3,4,5 has no repeats, and Y as 6,9,7,11,8 also has no repeats.\r
\n" ); document.write( "\n" ); document.write( "And no numbers are left out.\r
\n" ); document.write( "\n" ); document.write( "And yet a horizontal line will pass through the graph twice, Ie, between 6 and 9 is 7.\r
\n" ); document.write( "\n" ); document.write( "I must be thinking about this wrong. Or is it correct to say that it is not the graph LINE that matters with the horizontal line test, it is just the actual points on that graph that must not be intersected by a horizontal line? ? \n" ); document.write( "

Algebra.Com's Answer #761706 by Boreal(15235) $\"\"$ $\"About$

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That is correct. If these were points on a curve, it would not be 1:1, but as individual points, as long as one of them does not share two values of the other (a single y can't be defined by 2 different x values) then it is 1:1. \n" ); document.write( "

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