a = b

a

^{2}= ab

a

^{2}- b

^{2}= ab-b

^{2}

(a-b)(a+b) = b(a-b)

a+b = b

b+b = b

2b = b

2 = 1

Step 5 is dividing each side by (a-b), but it was established that a=b in the first line, so this is a divide by zero, which is not allowed in math. Once you've divided by zero, you can get the numbers to say whatever you want. There are longer examples that try to hide the divide by zero better, but the basic idea in all these is to break a rule discretely.

Card tricks are similiar. Early on you ascertain the identity of the card, by forcing a particular card on the volunteer, or sneaking a peek, or using a plant. Once you know, you can do any audacious thing to seemingly stack the deck against you. The volunteer can shuffle. You can turn your back. Whatever audacious bet you take doesn't matter, because by that point you already know the card.

And if you can do it in math, and in cards, you can do it in conversation. Once you let in a single faulty assumption or implication, you can move very far from the truth. Which isn't to say a single mistake automatically makes you wrong...using divide by zero you generate 1=1 as easily as 1=2. Unlike math, you can also be a little wrong but basically right in an argument. But it's important to remember when evaluating arguments or predictions about the future. A whole long string of reasoning can be airtight, but if there was one hand-waved fact (let's assume X for a second) all the subsequent arguments don't really matter.

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