Math Card Trick

Ask someone to choose a card.
Ask them to remember it's numerical value
(Ace = one, Jack = 11, Queen = 12, King = 13).
And also to remember the suit of the card.

  Tell them to
...double the value of the card.
...add three to the total.
...multiply the result by five.

  Now, tell them if the card is
...a diamond they must add one.
...a club they must add two.
...a heart they must add three.
...a spade they must add four.

Ask them for their final total.
And tell them their card from their total.

  The Secret:
The total will have two or three digits.
Mentally subtract 15 from their total.
The last digit gives the suit
(diamonds 1, clubs 2, hearts 3, spades 4.)
while the first number(s) gives the suit.

  Example: Jack of clubs
11 doubled is 22, add 3=25,
multiply by 5=125, add 2 for clubs=127.
Subtract 15 mentally, the result is 112.
Last number (2) means clubs,
first number (11) means Jack.

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Four Equals Five

Four is equal to five
To prove that 4 = 5.
Since,
-20 = -20
16 - 36 = 25 - 45
4^2 - 9*4 = 5^2 - 9*5
4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4
(4 - 9/2)^2 = (5 - 9/2)^2
4 - 9/2 = 5 - 9/2
4 = 5
What is wrong here?

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Equal Numbers

All Numbers are Equal
To prove all numbers are equal.
Choose a & b, and let t = a + b. 
Then
a + b = t
(a + b)(a - b) = t(a - b)
a^2 - b^2 = ta - tb
a^2 - ta = b^2 - tb
a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4
(a - t/2)^2 = (b - t/2)^2
a - t/2 = b - t/2
a = b
Thus, all numbers are equal. Why?

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Four Equals Three

Four Equals Three?
Let us prove that 4=3.
Suppose:
a + b = c
Then
4a - 3a + 4b - 3b = 4c - 3c
Rearrange terms
4a + 4b - 4c = 3a + 3b - 3c
Remove constants
4 * (a+b-c) = 3 * (a+b-c)
Remove brackets
4 = 3
What is wrong here?

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