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Equal positive integers
Theorem: All positive integers are equal.Proof: Sufficient to show that for any two positive integers, A and B, A = B.Further, it is sufficient to show that for all N > 0, if A and B
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Numbers equal zero
Theorem : All numbers are equal to zero.Proof: Suppose that a=b. Thena = ba^2 = aba^2 - b^2 = ab - b^2(a + b)(a - b) = b(a - b)a + b = ba = 0Furthermore if a + b = b, and a = b, then b + b
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Three is equal to four
Theorem: 3=4Proof:Suppose:a + b = cThis can also be written as:4a - 3a + 4b - 3b = 4c - 3cAfter reorganizing:4a + 4b - 4c = 3a + 3b - 3cTake the constants out of the brackets:4 * (a+b-c) =
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Dollars equal cents
Theorem: 1$ = 1c.Proof:And another that gives you a sense of money disappearing.1$ = 100c= (10c)^2= (0.1$)^2= 0.01$= 1cHere $ means dollars and c means cents. This one is scary in that I
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Dollars equal ten cents
Theorem: 1$ = 10 centProof:We know that $1 = 100 centsDivide both sides by 100$ 1/100 = 100/100 cents=> $ 1/100 = 1 centTake square root both side=> squr($1/100) = squr (1 cent)=>
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N equals N plus one
Theorem: n=n+1Proof:(n+1)^2 = n^2 + 2*n + 1Bring 2n+1 to the left:(n+1)^2 - (2n+1) = n^2Substract n(2n+1) from both sides and factoring, we have:(n+1)^2 - (n+1)(2n+1) = n^2 - n(2n+1)Adding
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One plus one are two
Theorem: 1 + 1 = 2Proof:n(2n - 2) = n(2n - 2)n(2n - 2) - n(2n - 2) = 0(n - n)(2n - 2) = 02n(n - n) - 2(n - n) = 02n - 2 = 02n = 2n + n = 2or setting n = 11 + 1 = 2
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Four is equal to five
Theorem: 4 = 5Proof:-20 = -2016 - 36 = 25 - 454^2 - 9*4 = 5^2 - 9*54^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4(4 - 9/2)^2 = (5 - 9/2)^24 - 9/2 = 5 - 9/24 = 5
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All numbers are equal
Theorem: All numbers are equal.Proof: Choose arbitrary a and b, and let t = a + b. Thena + b = t(a + b)(a - b) = t(a - b)a^2 - b^2 = ta - tba^2 - ta = b^2 - tba^2 - ta + (t^2)/4 = b^2 - tb
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One is negative one
Theorem: 1 = -1Proof:1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1Also one can disprove the axiom that things equal to the same thing are equal to each other.1 = sqrt(1)-1 =
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Log negative one zero
Theorem: log(-1) = 0Proof:a. log[(-1)^2] = 2 * log(-1)On the other hand:b. log[(-1)^2] = log(1) = 0Combining a) and b) gives:2* log(-1) = 0Divide both sides by 2:log(-1) = 0
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Proof E equal to one
Theorem: e=1Proof:2*e = f2^(2*pi*i)e^(2*pi*i) = f^(2*pi*i)e^(2*pi*i) = 1Therefore:2^(2*pi*i) = f^(2*pi*i)2=fThus:e=1
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One equal to one half
Theorem: 1 = 1/2:Proof:We can re-write the infinite series 1/(1*3) + 1/(3*5) + 1/(5*7) + 1/(7*9)+...as 1/2((1/1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + (1/7 - 1/9) + ... ).All terms after 1/1
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Crocodile is longer
Prove that the crocodile is longer than it is wide.Lemma 1. The crocodile is longer than it is green: Let's look at the crocodile. It is long on the top and on the bottom, but it is green
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Math is turning bad
"Psst, c'mere," said the shifty-eyed man wearing a long black trenchcoat, as he beckoned me off the rainy street into a damp dark alley. I followed."What are you
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Refrigerate elephants
Analysis:1. Differentiate it and put into the refrig. Then integrate it in the refrig.2. Redefine the measure on the referigerator (or the elephant).3. Apply the Banach-Tarsky
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Two plus two is five
"First and above all he was a logician. At least thirty-five years of the half-century or so of his existence had been devoted exclusively to proving that two and two always equal
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Debate about the box
An engineer, a physicist, and a mathematician are trying to set up a fenced-in area for some sheep, but they have a limited amount of building material. The engineer gets up first and makes
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Story about infinity
A very large mathematical convention was held in Las Vegas. The conventioneers filled two hotels, each with an infinite number of rooms. The hotels were across the street from each other
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The math one-liners
Math problems? Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x]. If parallel lines meet at infinity - infinity must be a very noisy place with all those lines crashing together!Maths Teacher: Now
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