In an "improper" one of these, the numerator is greater than the denominator
Fraction
As the name suggests, the $100 million Breakthrough Listen is a project to detect this type of signal from distant planets
Radio
Chester Carlson's photocopying process was rejected by over 20 companies before this one bought it & made him rich
Xerox
According to Rolling Stone, the best album of the decade:
"Nevermind"
Nirvana
He helped make the Teamsters the USA's largest labor union, but his whereabouts are a mystery
Jimmy Hoffa
In the expression 25, 2 is the base & 5 is this, the power to which 2 is raised
The Exponent
The area around a star where conditions are "just right" for life is called this zone, after a fairy tale girl
Goldilocks
The Fifth Amendment guarantees that no person shall be "deprived of life, liberty, or property, without" this
Due Process
"Mama Said Knock You Out"
LL Cool J
On Oct. 14, 1066 King Harold was killed at this battle
Hastings
The fundamental theorem of arithmetic says all composite numbers can be expressed as a product of these,
e.g. 65 = 5 x 13
Prime Numbers
A purported UFO crash in this southwest city in 1947 has spawned great interest & an annual festival
Roswell
Darwin wrote that he called a process this "or survival of the fittest"
Natural Selection
1992's Grammy-winning Album of the Year: this Brit's
"Unplugged"
Eric Clapton
This abolitionist wrote "The Battle Hymn Of The Republic", the semiofficial song of the Union Army
(julia Ward) Howe
The counting numbers beginning 1, 2, 3... are also known as these alliterative "numbers"
Natural
A British project to develop a spacecraft capable of reaching a nearby star within 50 years is named for this mythic Greek flyer
Icarus
In the Catholic church, this part of the canonization process gives the holy person the title "blessed"
Beautification
"Mellon Collie and the Infinite Sadness"
Smashing Pumpkins
In 1825 Charles X of France finally recognized this nation, 21 years after it declared its independence
Haiti
This law of addition says x + y = y + x
Commutative
A theoretical basis of alien life is this 2nd most common element in Earth's crust; scientists have made enzymes bond it to carbon
Silicon
In the 1830s this Frenchman developed a new photo process that cut exposure time from 8 hours to less than 30 minutes
Daguerre
"Vitalogy", featuring "Better Man"
Pearl Jam
As many as 30,000 of these German mercenaries fought during the American Revolution & some were with Cornwallis when he surrendered
Hessians