 # [Official] Nerdy Math Topic

isn’t it 11?

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searched the web: over 360 pages to prove definitively that 1 + 1 = 2…

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Basically, 1 + 1 indeed equals to 2 because of a simple formula called addition, which is like a simple operation of arithmetic. Basically, you take any number (x) and add it by a different number (y). Addition gives a sum depending on what x and y is by adding them together. That’s why it is called addition.

In this case, we have 1 + 1. Here, we simply add 1 (y) to 1 (x), and that equals to two. This could be hard to understand at first, but people usually find it better if we demonstrate in word problems.

So for example, if there were 1 red apple (x) and 1 green apple (y), there would be 2 apples. If you still do not understand, I suggest you learn how to count first, because then it would be easier to understand this equation.

When counting integers, there’s usually a sequence with a common difference between each other of 1. Like 1, 2, 3, 4. These are each symbols for each number. Here’s the formula for finding the next number. N (current number) + d (common difference). This can be used to find the next number, but you would still need to understand the symbol that represents it (in this case, 5). Although I won’t dive further into this, I really suggest looking into this before we talk about arithmetic.

Now that we understand counting and the symbols that represent the numbers (1, 2, 3…) we can go back to addition. Basically, we add one number (in this case 1) to another (which is also 1). It’s really quite simple once you get it. We take 1, and add another 1 to it, like the formula I talked about in counting (N + D).

The reason I had a variable next to the numbers in paragraph 2 is because of course these numbers could vary, but that gets a little confusing, because we would have to use calculation. For example, we would have 1 (x) + 2(y). Here, we would add the common difference (2) to 1. If we wen’t back to the sequence that we looked at earlier, that would be 3.

1 (+1)
2 (+1)
4

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wow very nerdy

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Well, you first need to define what 2 is. The definition of two is the cardinality (size) of a set {x,y} where x doesn’t equal y.
If you take two disjoint sets and take their union (by definition, adding their cardinalities), for example {x} and {y}, you get a set {x,y}. Since x doesn’t equal y, the cardinality of the union is what we defined 2 to be.
This isn’t a complete “proof”, as I didn’t prove everything here, but this should give you the basic idea.

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What is 1+x2

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1 + x^2 or just 1 + x2?

1 + x^2 I can’t solve Bc it’s a variable

1 + x2 = 5 (1 + (2 x 2))

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This is something my class bought up during math and I’m interested in hearing your opinions.

What is 0^0?

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undefined

0 to any power is 0, and any number to the power of 0 is 1. 1 doesn’t equal 0, so it’s undefined

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Exactly!

But there are some mathematicians that argue that 0^0 is 1.

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Well they’re just 3 Likes

I know right lol!

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That’s a very interesting question. The definition of exponentiation of natural numbers once again goes back to cardinal arithmetic. Ie. a^b is equal to the number of functions from a set of size (cardinality) b to a set of cardinality a.
By that definition, 0^0 is equal to the number of functions from the empty set to the empty set. There actually exists one function like this, which is also the empty set. So 0^0=1.

If you use the binomial theorem, and you expand (x+0)^n you’ll get x^n * 0^0, so 0^0 must be defined as 1 here in order for the binomial theorem to not suddenly fail for specific cases.

By the power rule, the derivative of f(x)=x is 1 x^0. We know that the derivative of f(x)=x is 1, even when x=0, so in this case defining 0^0=1 is helpful.

There are other cases where 0^0 can have another value, but they mostly have to do with limits. For the most part though, many mathematicians have defined 0^0 to be 1 for simplicity. If you go plug in 0^0 on googles calculator for example, it’ll tell you 1.

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This isn’t the definition for exponentiating 0. You could think of this as a theorem, but you’d have to prove it for the special case of 0^0.

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Ohh ok! That makes more sense!

So I guess u just need to think of it as a theorem…

I’m gonna explain my understanding of 0^0= 1 in my next math class. Thanks for the explanation!

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Um so I’ve got an isosceles triangle (both sides are equal).

The known measurements are the base width and the height. How do I calculate the sides length and angles?

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You can use ye Pythagorean theorem for the side lengths and trigonometric functions for the angles.

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First, divide the base in half, which gives you 2 right triangles. Then you can use Pythagorean theorem & trig as The_Vast_Void said.

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What’s 10 x 2

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20

Is this a trick question in any way?

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