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*From*: John Denker <jsd@av8n.com>*Date*: Sun, 12 Nov 2017 12:24:42 -0700

On 11/12/2017 10:07 AM, Bob Sciamanda via Phys-l wrote:

An interesting QUORA discussion ==>

https://www.quora.com/What-is-the-importance-of-irrational-numbers

Uncle Albert famously said:

As far as the laws of mathematics refer to reality, they are not

certain; and as far as they are certain, they do not refer to

reality.

The mathematicians in the quora discussion seem to

have lost sight of that.

Mathematicians are free to construct their own little

worlds in which exactitude is required. However, when

they try to justify their constructions in terms of

real-world activities, such as throwing things in the

air, they are seriously out-of-bounds.

A child can throw a ball without irrational numbers.

Indeed, humans can build rockets and fly to the moon

without rational numbers. Hint: floating-point

arithmetic suffices for designing sports equipment,

spacecraft, et cetera, and does not use irrational

numbers.

The claim that irrationals are required for calculus

is wrong even by mathematical standards. You can take

the limit as b goes to zero by writing b as a rational

and letting the denominator become very large.

Irrationals are important to the /history/ of human

thought, because a bunch of ancient Greeks made a

big fuss over integers, rationals, exactitude, and

completeness. They even built a religious cult and

a political party around that. There was a big stink

when it was proved that the rationals did not suffice

to represent exact, complete solutions to certain

equations. This was an early example of the power

of rigorous /proof/ to prove unexpected results.

Spectacularly unexpected.

**References**:**[Phys-L] Irrationals***From:*"Bob Sciamanda" <treborsciamanda@gmail.com>

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