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Leonhard Euler
Infinity Minus Infinity
Seden Nalbant
Any number subtracted from itself is equal to zero. Therefore, you might think that infinity minus infinity is also equal to zero; however, this is not true. Let’s find out the answer together.
First let’s assume that infinity minus infinity is equal to zero.
∞ - ∞ = 0
Adding one to both sides of the equation:
∞ - ∞ + 1 = 0 + 1
Simplified we get the following equality:
∞ - ∞ = 1
This would mean that ∞ - ∞ is equal to both one and zero, which simply can’t be true. Substituting one with any other number results in ∞ - ∞ being equal to any real number. For this reason, ∞ - ∞ is undefined. Taking a different approach, we’ll prove that it is undefined.
Let’s assume the previous equation to be true again:
∞ - ∞ = 0
We know ∞ + ∞ = ∞ to be true, so let’s substitute it in the equation.
∞ + ∞ - ∞ = 0
Because we already assumed ∞ - ∞ = 0, we can substitute it in the equation:
∞ + 0 = 0
Which is then simplified to:
∞ = 0
This simply cannot be true, hence:
∞ - ∞ = undefined
References
Phil for Humanity. “What Does Infinity Minus Infinity Equal?” Phil for Humanity, Phil for Humanity, 1 Jan. 2010, https://www.philforhumanity.com/Infinity_Minus_Infinity.html.
“What Is the Result of ∞ - ∞?” GeeksforGeeks, 28 June 2021, https://www.geeksforgeeks.org/what-is-the-result-of-%E2%88%9E-%E2%88%9E/.
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