Real Numbers And Their Chain Of Inequalities

Algebra Level 3

\[(A){ \quad x\, \, { < }\, \, x }^{ 2 }\, \, { < }\, \, { x }^{ 3 }\\ { (B)\quad x\, \, { < }\, \, x }^{ 3 }\, \, { < }\, \, { x }^{ 2 }\\ { (C)\quad x }^{ 2 }\, \, { < }\, \, x\, \, { < }\, \, { x }^{ 3 }\\ { (D)\quad x }^{ 2 }{ \, \, { < }\, \, x }^{ 3 }\, \, { < }\, \, x\\ (E)\quad { x }^{ 3 }\, \, { < }\, \, { x\, \, { < }\, \, x }^{ 2 }\\ (F){ \quad x }^{ 3 }{ \, \, { < }\, \, x }^{ 2 }\, \, { < }\, \, x\]

If \(x\) is a real number, how many of the above inequalities can be true?


Inspiration.

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