# A diagram of some useful constants

Some harmonic constants.

# Some diagrams for relative velocities achieved by jet engines

# Does the Harmonic series converge or diverge in the ‘real’ world?

https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)

“In mathematics, the harmonic series is the divergent infinite series:

It is well known that the Harmonics series diverges in the pure world (see above).

Does it also converge to a finite value in the ‘real’ world? I think so. Anyone want to disagree?

Using ≜ to indicate an origin then:-

The pure number range for the Integer series is

± {∞:n/1:1:≜}

the pure number range for the Harmonic series is

± {∞:1/n:1:≜}

These 2 can be combined to produce all floating point numbers.

± {∞:f/1:1.0:1/f}, ± {∞:f/1:{≜}:1/f}

The number ranges that are practical (real) to work with, measured in SI units, are only a sub-set of the above though

± {limit:n/1:1:≜}

and

± {limit:1/n:1:≜}

Therefore, by replacing the usual work in n/1, and by keeping track of the scales and meanings that have been applied, one can work simpler in 1/n to whatever resolution and precision the limit to limit range implies.

This also goes for all constants chosen from ± {∞:n/1:1:≜} such as π, √2, e and i.

≜ is often called/replaced by 0.

One lays over the other to provide an origin to the number series if including 0 is all.

It is much simpler, faster and more detailed to work in 1/n, even for y ≜ f(x), with limits properly applied that is.

This removes 0 from consideration as it is replaced by a range scale change.

0 and ∞ can then be correctly reported as an error as they cannot be reproduced in ± {limit:1/n:1:≜}

A pure ± {0:1} 1/SI units world. https://en.wikipedia.org/wiki/SI_base_unit

This then means that the Harmonic series converges to a finite value in the ‘real’ world determined by the measurement limits/length to the number of digits used to record the data.

# Some charts to ponder, from the year 2000

Population

GDP (%)

Wealth

# I am a Unary operator (a person/robot)

I follow all Unary mathematics and operations. (and any moral responsibilities for my definitions, associations and actions).

https://en.wikipedia.org/wiki/Moral_responsibility

# Some additional diagrams that you may find useful

Fig 8. Power (square)

Fig 9. Square root

Fig 10. y = f(x) centred at the origin for 1.5d.

Fig 11. A simple square

Fig 12. A simple circle

Fig 13. An ellipse

Fig 14. A sine wave.

Fig 15. A cosine wave.