2+2 = what is annwer
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and 4
is the answers
and 4
is the answers
sumanGeorge:
only 4
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Well, 2 + 2 is........ { A hypothetical question }
Normally, we'd say 4...... but how ???
Let's see ---->
Two plus two equals four
Proof: -->
The set of integers is an (infinite) group with respect to addition.
Since 2 is an integer, the sum of 2 and 2 must also be an integer.
Suppose, for the sake of contradiction, that 2 + 2 < 4.
We have 2 > 0. Adding two to both sides, we get
2+2 > 0+2
Since 0 is the identity element for addition, we have 2 + 2 > 2.
Hence 2 < 2 + 2 < 4 so 2 + 2 must equal 3.
Since 3 is prime, by Fermat’s Little Theorem,
we have the following for a ∈ :
≡ 1 (mod 3)
=>
≡ 1 (mod 2 + 2)
But
=
a³ / a
=
a × a × a /
a
= a × a
and, for a = 2,
2 × 2 ≡ 0 (mod 2 + 2)
Since, by the definition of multiplication, 2 × 2 = 2 + 2
So, we have
≡ 0 (mod 2 + 2)
≡ 0 (mod 2 + 2)
This is a contradiction to Fermat’s Little Theorem, so 2 + 2 must not be prime. But 3 is prime.
Hence 2+2 must not equal 3, and therefore 2+2 ≥ 4.
It remains to show that 2 + 2 is not greater than 4.
To prove this we need the following lemma:
Lemma 1. ∀a ∈ Z, if a > 4, ∃b ∈ Z such that b > 0 and a − 2 = 2 + b.
If a were a solution to the equation 2 + 2 = a, then we would have a − 2 = 2 + 0. The lemma states that this cannot hold for any a > 4, and so a = 4, as desired. Therefore, 2 + 2 = 4
Hope you'd have the Answer next time a Horrible friend asks IF 2 + 2 = 4 ...... How????
Normally, we'd say 4...... but how ???
Let's see ---->
Two plus two equals four
Proof: -->
The set of integers is an (infinite) group with respect to addition.
Since 2 is an integer, the sum of 2 and 2 must also be an integer.
Suppose, for the sake of contradiction, that 2 + 2 < 4.
We have 2 > 0. Adding two to both sides, we get
2+2 > 0+2
Since 0 is the identity element for addition, we have 2 + 2 > 2.
Hence 2 < 2 + 2 < 4 so 2 + 2 must equal 3.
Since 3 is prime, by Fermat’s Little Theorem,
we have the following for a ∈ :
=>
But
and, for a = 2,
2 × 2 ≡ 0 (mod 2 + 2)
Since, by the definition of multiplication, 2 × 2 = 2 + 2
So, we have
This is a contradiction to Fermat’s Little Theorem, so 2 + 2 must not be prime. But 3 is prime.
Hence 2+2 must not equal 3, and therefore 2+2 ≥ 4.
It remains to show that 2 + 2 is not greater than 4.
To prove this we need the following lemma:
Lemma 1. ∀a ∈ Z, if a > 4, ∃b ∈ Z such that b > 0 and a − 2 = 2 + b.
If a were a solution to the equation 2 + 2 = a, then we would have a − 2 = 2 + 0. The lemma states that this cannot hold for any a > 4, and so a = 4, as desired. Therefore, 2 + 2 = 4
Hope you'd have the Answer next time a Horrible friend asks IF 2 + 2 = 4 ...... How????
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