Infinity / Infinity = ? ```Name: n scherer Status: N/A Age: N/A Location: N/A Country: N/A Date: Around 1995 ``` Question: If you divided Infinity by Infinity would you not get 1? If not, could you explain why? Replies: In the real number system, "INF(INITY)" is not considered to be one of the set of real numbers and so none of the operations are defined for INF. Even in systems where some kind of INF is included (complex numbers in some contexts) we still see avoidance of defining INF/INF because quotients supposedly are related to products in a unique way. For example, define a/b = c if c is the unique number solving the equation a = bx. If we define a*INF = INF for all non-zero a (as is reasonably done in some cases) then INF/INF is not uniquely definable. teeIn addition to the previous remarks, INF/INF does seem to occur as the result of taking limits. For example, let us divide 1 + x^2 by 1 + x^4 and ask for the ratio in the limit that x-->INF (x becomes infinite). Although the question seems to involve the ratio, INF/INF, the answers is uniquely zero. You might try working out some other examples that give different numbers for the answer. Try, for example, the ratio of 1 + 3x^2 divided by 1 + x^2 in the limit that x becomes infinite. jlu Click here to return to the Mathematics Archives

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