Algebraic Properties
Reflexive property
For any real number a, a=a
1283+4827
6110
Known as the ‘Father of Geometry,' this mathematician laid the foundations for geometry with his work.
Euclid
Explain the pattern.
6=>3. Each number corresponds to the number of letters it has.
What number is twice the sum of its digits?
18
Transitive property
If a=b and b=c, a=c
10+9+8+6+5+4+3+2+1
48
A great Italian mathematician whose famous recursive sequence illuminates the mathematical structures of nature and the natural world.
Fibonacci
The infinity of the natural numbers and that of the even numbers is the same
What number is twice the sum of its digits?
18
Distributive Property
a(b+c) = ab + ac
10^4-10^3+10^2-10^1+10^0
9091
Known as the Father of Modern Computing, this mathematician's work blazed a trail for modern computers as we know them today. He introduced the concept of a universal machine that could perform thousands of calculations based on predetermined rules/instructions. His work was invaluable in WW2 when he helped decode the German Enigma code.
Alan Turing
Jack is looking at Anne. Anne is looking at George. Jack is married, George is not, and we don’t know if Anne is married. Is a married person looking at an unmarried person?
Yes.
Using only an addition, how do you add eight 8’s and get the number 1000?
888+88+8+8+8=1000
Additive property
10!*5!/(7!*2^5)
2700
One of the most famous modern mathematicians, he is known for his substantial breakthroughs and research on the topics of representation theory, harmonic analysis, combinatorics, and partial differential equations.
Terence Tao
In a group of 23 people, what is the probability that two will share the same birthday?
50%
An airplane has 100 seats numbered from 1 to 100, and there are 100 passengers boarding the plane in a random order. Each passenger has a boarding pass with his/her seat number on it. The first passenger who boards the plane didn't bother to look at his boarding pass, so he just picked a seat at random. For each subsequent passenger, if the assigned seat is available, that passenger takes the correct seat. But if it's already occupied, then the passenger chooses from any other remaining seat randomly. What is the probability that the last passenger sits in the correct seat?
50%
Multiplicative Property
If a=b, a*c = b*c
17*sqrt(529)
391
This mathematician excelled in the development of coordinate systems for specific purposes; he applied the techniques of calculus to analyze geometrical problems and proved the relationship between vertices, edges, and faces for convex polyhedra.
Euler
Six distinct integers are picked at random from {1,2,3,...10}. What is the probability that, among those selected, the second smallest is 3?
1/3
Prove the square root of two is irrational
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