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has added a new journalThis is laid out here threadbare, and explanations will come if asked for.
Given: This is Mathematicians Village
Suppose: Everyone understands Mathematical Induction
Corollary: If someone doesn't understand, they'll ask 'bout it.
Prove: 1=2
(This has to be done using algebra no more complex than high-school-level.)
Let: x = 1
=> (implies that) x=x
=> x^2 = x^2 (squares of equal amounts)
=> x^2 - x^2 = x^2 - x^2
=> (x^2 - x^2) = (x-x)(x+x) (product of two squares)
=> x(x-x) = (x+x)(x-x) (removing x as a common element from both sides)
=> x = (x+x)
Now lets say x = 1
=> 1 = 1+1
=> 1 = 2
Hence the very foundation of mathematics stands disproved. Anyone care to offer an explanation as to how this is possible?)
Explanations:
(product of two squares)
=> (a-b)(a+b) = a^2 + ab - ab - b^2
=> (a-b)(a+b) = a^2 - b^2
Superman
My my, caught by the first comment.. Subhaan Allah - we are blessed indeed.Einstein said: "Sometimes it takes a real genius to see the blindingly obvious."
Are we really in blessed company?-}
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has added a new journalYou have probably worked through advanced calculus, differential equations, state space equations, and vector algebra, but let?s see if you can do some elementary math.
Note: This calculation must be done in your head only and not using paper and pen.
Try it:
Take 1000 and add 40 to it.
Now add another 1000.
Now add 30.
Another 1000.
Now add 20.
Now add another 1000.
Now add 10.
What is the total? Scroll down for answer.
Did you get 5000? Well, the correct answer is actually 4100. Don't believe it? Check with your calculator. The decimal sequence confuses our brain, which always jumps to the highest decimals (100s instead of 10s).