The fun tab on my website.

Just some fun stuff on here. Not sure how often I'll post on here, it depends. I guess just check here occasionally.

How can 1=2?

• Let's make 1=a and 2=b, so that a=b.
• If one number equals another, then those numbers multiplied by the same number should produce the same result. If this is the case, then a^2=ab, since a multiplied by a should equal b multiplied by a according to the theory stated.
• Similar to our theory above, if two numbers that are equal to each other subtract the same number, it should produce the same result. In this case, we will subtract b^2 from both sides (specifically b^2 because it will help us later.)
• Do you see how you can factor each expression now? a^2-b^2 equals (a+b)(a-b) beacuse of the perfect square theory. ab-b^2 has a greatest common factor, which is b. When you factor out the greatest common factor, you get b(a-b).
• Do you see a similar binomial on each side of the expression. That's right, it's (a-b). Now we must divide the equation by (a-b) since it's present on both sides, which would cancel it out.
• After doing the step above, we are left with a+b=b. Now if a=b, then replacing b with a should result in the same number, yes? Well, let's try it: a+b=b --> a+a=a. This gives us 2a=a.
• Now, if a=1, which was assigned at the start of the problem, then 2(1)=1. This means that 2=1!
• Are you able to find the problem in this? Try to guess. If not, I will provide a link below explaining how this can't be true.

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Here's how to make a list:

• First thing
• Second thing
• Third thing

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