<% tp.file.cursor() %>
“Stacked tilde” usually means you’ve seen one tilde sitting on top of another tilde (≈ a double-deck wavy line), not just two typed side by side like ~~.
Single Tilde (~)
-
Approximation: “π ~ 3.14” means “π is about 3.14.”
-
Similarity in geometry: △ABC ~ △DEF means triangles are similar.
-
Distribution notation in statistics: X \sim N(0,1) means “X is distributed as Normal(0,1).”
-
Logic (older notation): ¬P can be written as ~P (negation).
Stacked Tilde (≈)
The stacked or double tilde is a separate mathematical symbol, not just two typed tildes. You’ll usually see it typeset as ≈.
-
“Approximately equal”:
2 + 2.001 \approx 4 → more formal than a single tilde.
-
Greater precision in meaning: single tilde is more “loosely similar/related,” while the stacked tilde is reserved for “numerical approximation” or “almost equal.”
-
Unicode code point: U+2248 (≈). On most keyboards you can type it as \approx in LaTeX.
Summary
-
~ → about, distributed as, similarity, negation, home directory (in shells).
-
≈ (stacked tilde) → specifically “approximately equal to” in mathematics.
So: a single tilde is vague and multipurpose, while the stacked tilde is precise math shorthand for “approximately equal.”