The professor dealt with a various methods of proving
statements this week. Honestly, I could know the exact meaning of ⌊x⌋ through this course. Actually, I didn't
know that "∀x ∈
R y = ⌊x⌋"
has this complicated symbolic meaning "y ∈ ℤ ∧ y ≤ x ∧ (∀z ∈ ℤ, z ≤ x ⇒ z ≤ y)" and
conclusively, "∀x
∈ ℝ, ⌊x⌋ ﹥ x -1".
I realized that the symbolic expression which seems
very simple could contain a complicated and sophisticated meaning in it.
Next week is reading week! I think I should read some
reference books about proof and review mathematical terminologies for the next
step, especially I am going to check the terms such as б, ԑ, ⌊x⌋, ⌈x⌉ and so on.
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