Comment on Why don't we define “imaginary” numbers for every “impossibility”? (2012)parentComments−comte70923y1 / 0 = +infinity Implies that 0 * +infinity = 1, so it does run into make of the same issues.There are instances that make it useful, but the extended real number line isn’t used heavily in practice.−Grustaf3yYou might not have much use for the real projective line when tallying up prices in the grocery store, but projective geometry is definitely very useful. https://en.wikipedia.org/wiki/Projective_geometry−tshaddox3yYeah, I don't really see what this gets you. With basic real number division you have to make the exception for zero in the definition: a/b = c if and only if a = c*b and b!=0 And with this infinity thing you just have to make essentially the same exception for multiplication and infinity: c*b = a if and only if a/b = c and b!=infinity and c!=infinity−hgsgm3yWhat is the "issue"?"/" means "* reciprocal of".If "infinity" is defined as "reciprocal of 0", what is the problem?Yes it is an exception to 0*n=0.It won't work in every setting, but it works in some settings, like inversive geometry.−scotty793yIn normal math 1/0 is undefined but in a math where 1/0 is defined to be inf the 0*inf is still undefined.
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1 / 0 = +infinity Implies that 0 * +infinity = 1, so it does run into make of the same issues.
There are instances that make it useful, but the extended real number line isn’t used heavily in practice.
You might not have much use for the real projective line when tallying up prices in the grocery store, but projective geometry is definitely very useful. https://en.wikipedia.org/wiki/Projective_geometry
Yeah, I don't really see what this gets you. With basic real number division you have to make the exception for zero in the definition:
And with this infinity thing you just have to make essentially the same exception for multiplication and infinity:What is the "issue"?
"/" means "* reciprocal of".
If "infinity" is defined as "reciprocal of 0", what is the problem?
Yes it is an exception to 0*n=0.
It won't work in every setting, but it works in some settings, like inversive geometry.
In normal math 1/0 is undefined but in a math where 1/0 is defined to be inf the 0*inf is still undefined.