My brothers was to teach me the basics that chathamtownfc.netematics and we had actually some confusion about the optimistic and an adverse behavior the Zero. After reading a few post ~ above this we involved know that it depends on the paper definition of its use.

Why do we take it 1/0 as confident infinity quite than negative infinity (we come close come zero from an unfavorable axis)?

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The various other comments space correct: \$frac10\$ is undefined. Similarly, the limit of \$frac1x\$ together \$x\$ ideologies \$0\$ is additionally undefined. However, if you take it the border of \$frac1x\$ together \$x\$ viewpoints zero indigenous the left or native the right, friend get negative and confident infinity respectively.

\$1/x\$ does tend to \$-infty\$ as you technique zero from the left, and also \$infty\$ as you approach from the right:

That these boundaries are not equal is why \$1/0\$ is undefined.

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The place where you frequently see \$1 colorred/ 0 = infty\$ is when doing arithmetic in the projective line. (I"ve added color come \$colorred/\$ to much better distinguish it from the ordinary department operation top top the genuine numbers) The binary operation \$colorred/\$ is defined for every pair the projective real numbers except \$(0,0)\$ and also \$(infty, infty)\$:

\$ x colorred/ y = x/y\$ once \$y eq 0\$\$ x colorred/ 0 = infty\$\$ x colorred/ infty = 0\$\$infty colorred/ x = infty\$

where \$x,y\$ represent ordinary real numbers. (one can define the various other arithmetic to work too)

The projective line has actually only one unlimited element. In the projective line, the same number \$infty\$ is at both "ends" that the plain line. Over there is another common number mechanism -- the prolonged real number -- that has two limitless elements: \$+infty\$ and \$-infty\$. Make details note that \$1 colorcyan/ 0\$ is undefined because that the arithmetic of extended real numbers. (where again I"ve added color come distinguish)

Unfortunately, people often usage \$infty\$ instead of \$+infty\$. So, when someone writes \$infty\$, it have the right to be unclear whether or no they room doing arithmetic in the projective genuine line, or in the expanded real line.