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Addition/Multiplication/Power/N/Injectivity/Exercise
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Is the mapping
φ
:
N
+
×
N
+
⟶
N
+
×
N
+
×
N
+
,
(
a
,
b
)
⟼
(
a
+
b
,
a
b
,
a
b
)
,
{\displaystyle \varphi \colon \mathbb {N} _{+}\times \mathbb {N} _{+}\longrightarrow \mathbb {N} _{+}\times \mathbb {N} _{+}\times \mathbb {N} _{+},(a,b)\longmapsto (a+b,ab,a^{b}),}
injective
, or not?
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