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Examples

The question was raised in [section 3.3], and we must indeed ask whether the realnumber spacetime continuity that is almost universally assumed in physical theories is really the appropriate mathematics for describing the ultimate constituents of Nature.

If you're thinking of numbers on a realnumber continuum, sure: 3 is "less than pi."
"Yes, our announcement post title is grammatically incorrect." Ann Althouse 2009

Similarly we could be misled by the representation of a concept as a number into thinking that there is naturally an infinitely extendable scale for that concept, since the realnumber line continues on to infinity in both directions.
Operationalism Chang, Hasok 2009

The same point can be put in terms of sentences: Frege insists that the consistencyquestion that arises for the sentences under their geometric interpretation is a different issue from the one that arises for those sentences under their realnumber interpretation; for Hilbert on the other hand, there is just one question, and it is answered in the affirmative if there is any interpretation under which the sentences express truths.
The FregeHilbert Controversy Blanchette, Patricia 2009

There are very few investors for whom a 0% return is just another arbitrary point on the realnumber spectrum.
Felix Salmon  All posts Felix Salmon 2010

There are very few investors for whom a 0% return is just another arbitrary point on the realnumber spectrum.
Financial Sector and Stocks Analysis from Seeking Alpha Felix Salmon 2010

SOLUTION 36 Consider g (x) ¼ 1/x, with the restriction that the domain and range can attain any realnumber value except zero.

Polar graph of a lemniscate centered at the origin, with radius a. THREELEAFED ROSE The general form of the equation of a threeleafed rose centered at the origin in the polar plane is given by either of the following two formulas: r ¼ a cos 3 r ¼ a sin 3 where a is a realnumber constant greater than 0.

LEMNISCATE The general form of the equation of a lemniscate centered at the origin in the polar plane is given by the following formula: r ¼ aðcos 2Þ1 = 2 where a is a realnumber constant greater than 0, representing the maximum radius.

CHAPTER 5 Polar Coordinates 81 CIRCLE CENTERED AT ORIGIN The equation of a circle centered at the origin in the polar plane is given by the following formula: r¼a where a is a realnumber constant greater than 0.
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