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Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

Schanuel's conjecture

In the mid 1960s American mathematician Stephen Schanuel devised a complex mathematical conjecture regarding the 'transcendence degree' of certain 'field extensions' of the rational numbers.

Formally stated :

Given any n complex numbers z1, โ€ฆ, zn that are linearly independent over the rational numbers Q, the field extension Q (z1, โ€ฆ, zn, ez1 , โ€ฆ, ezn) has transcendence degree at least n over Q

Source :Wikipedia

At present, the conjecture has neither been proved or disproved.

At present, the conjecture has neither been proved or disproved.
If it is eventually proved, it could have profound implications for exploring the nature of Irrational numbersplugin-autotooltip__plain plugin-autotooltip_bigIrrational numbers

unknowable

An irrational number is a real number that can't be expressed as a ratio of integers, i.e. as a fraction.

Put another way, it can never be specified with absolute accuracy.

Well known examples are ฯ€ and โˆš2

For many irrational numbers, relatively simple mathematical proofs exist which show that it's impossible to ever arrive at a finite solution. For example,
such as ฯ€ and the natural logarithm e.


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