Example
Every real x satisfies the inequality
where is the integer part function. By a typical application of the transfer principle, every hyperreal x satisfies the inequality
- ,
where * is the natural extension of the integer part function. If x is infinite, then the hyperinteger * is infinite, as well.
Read more about this topic: Transfer Principle
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)