How to Make a False Proof Using Infinity
Ask your friend what infinity plus one is., Write down the equation your friend just stated., Ask your friend what would happen if he or she subtracted ∞ from both sides., Let your friend review the proof again.
Step-by-Step Guide
-
Step 1: Ask your friend what infinity plus one is.
If your friend doesn't know, help him or her figure it out for him-/herself.
Don't give them the answer unless you really have to.
If your friend can't get it, ask him or her a more visual version of the question, for example: "If I had an infinite supply of apples and I add one more apple to the supply, how many apples are in my supply?" The answer is infinity. -
Step 2: Write down the equation your friend just stated.
∞ + 1 = ∞ , The formal name for this operation is called the subtractive property of equality.
What you are left with is 1 =
0. , He or she will want to look at it more closely and try to figure out what the flaw is.
He or she will probably fail.
You might feel inclined to laugh at your friend's bewilderment or make fun of him or her a little.
This would be a good time to do so.
The catch is that when you subtracted ∞ from both sides, your friend assumed that ∞
- ∞ =
0.
Because ∞ is not a real number, it follows its own set of rules.
Almost nobody knows this. ∞
- ∞ is indeterminate because some infinities are actually bigger than other infinities.
In this case, the infinity on the right side of the equation is inherently bigger than the one on the left. -
Step 3: Ask your friend what would happen if he or she subtracted ∞ from both sides.
-
Step 4: Let your friend review the proof again.
Detailed Guide
If your friend doesn't know, help him or her figure it out for him-/herself.
Don't give them the answer unless you really have to.
If your friend can't get it, ask him or her a more visual version of the question, for example: "If I had an infinite supply of apples and I add one more apple to the supply, how many apples are in my supply?" The answer is infinity.
∞ + 1 = ∞ , The formal name for this operation is called the subtractive property of equality.
What you are left with is 1 =
0. , He or she will want to look at it more closely and try to figure out what the flaw is.
He or she will probably fail.
You might feel inclined to laugh at your friend's bewilderment or make fun of him or her a little.
This would be a good time to do so.
The catch is that when you subtracted ∞ from both sides, your friend assumed that ∞
- ∞ =
0.
Because ∞ is not a real number, it follows its own set of rules.
Almost nobody knows this. ∞
- ∞ is indeterminate because some infinities are actually bigger than other infinities.
In this case, the infinity on the right side of the equation is inherently bigger than the one on the left.
About the Author
Brenda Gonzales
Brings years of experience writing about DIY projects and related subjects.
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