Euler's number

URI: https://gptkb.org/entity/Euler%27s_number
GPTKB entity
Statements (52)
Predicate Object
gptkbp:instance_of gptkb:electricity
gptkbp:approximately_equals 2.71828
gptkbp:base natural exponential function
natural logarithm
natural logarithm function
https://www.w3.org/2000/01/rdf-schema#label Euler's number
gptkbp:is_a_solution_for the equation f'(x) = f(x) for f(0) = 1
gptkbp:is_an_irrational_number nan
gptkbp:is_an_transcendental_number nan
gptkbp:is_defined_by limit of (1 + 1/n)^n as n approaches infinity
gptkbp:is_related_to gptkb:Euler's_formula
exponential function
gptkbp:is_the_limit_of (1 + 1/n)^n as n approaches infinity
(1 + x/n)^n as n approaches infinity for x=1
gptkbp:is_used_in gptkb:Mathematics
probability theory
differential equations
complex analysis
financial mathematics
compound interest calculations
gptkbp:symbol e
gptkbp:values e^0 = 1
ln(1) = 0
ln(e) = 1
e^(-1) = 1/e
e^(-x) for x=0
e^(1/2) = √e
e^(1/3) = e^(1/3)
e^(10) = e^10
e^(2) = e^2
e^(3) = e^3
e^(4) = e^4
e^(5) = e^5
e^(6) = e^6
e^(7) = e^7
e^(8) = e^8
e^(9) = e^9
e^(iπ) + 1 = 0 (Euler's identity)
e^(x) for x=0
e^(x) for x=10
e^(x) for x=2
e^(x) for x=3
e^(x) for x=4
e^(x) for x=5
e^(x) for x=6
e^(x) for x=7
e^(x) for x=8
e^(x) for x=9
e^1 = e
e^x for x=1
gptkbp:bfsParent gptkb:Leonhard_Euler
gptkbp:bfsLayer 4