assume (for simplicity) that vs the proof of that is provided

The two phrases are not directly comparable as they serve different purposes. "Assume (for simplicity) that" is used to introduce a simplifying assumption in a discussion or explanation. On the other hand, "the proof of that is provided" is used to indicate that evidence or justification for a statement is given. They are used in different contexts and cannot be interchanged.

Last updated: March 17, 2024 • 624 views

assume (for simplicity) that

This phrase is correct and commonly used in English to introduce a simplifying assumption in a discussion or explanation.

This phrase is used to set up a hypothetical scenario or assumption for the sake of simplifying a complex situation or argument.

Examples:

Assume, for simplicity, that the Earth is a perfect sphere.
Let's assume, for simplicity, that the cost remains constant.
Assume, for simplicity, that the population growth rate is linear.
For simplicity, assume that the system is in equilibrium.
Let's assume, for simplicity, that the process is reversible.

Show examples from the web [+]

Equilibrium in Perfectly Competitive Markets. (Assume for simplicity that all firms have access to the same technology and input markets, so they all have the ...
Also assume for simplicity that ACK packets are extremely small and can be ignored. (a) At least how big would the window size (in packets) have to be for the ...
Although our considerations will work for any (p, q)-torus knot with q > p > 0, we assume for simplicity that K is a (2,3)-torus knot, in order to keep the arguments ...
Consider two random variables X and Y . Assume for simplicity that they both have zero mean. (a) Show that X and E[X | Y ] are positively correlated. (b) Show ...

the proof of that is provided

This phrase is correct and commonly used in English to indicate that evidence or justification for a statement is given.

This phrase is used to signal that the evidence or reasoning supporting a particular claim or statement is being presented.

Examples:

The proof of that is provided in the following section.
In the next paragraph, the proof of that is provided.
The proof of that is provided through experimental data.
The proof of that is provided by mathematical analysis.
The proof of that is provided by citing relevant sources.

Show examples from the web [+]

Jun 8, 2005 ... rability property that characterizes (6) and (7). The proof of that is provided in Appendix. A. We now suppose that leisure and goods are superior ...
May 24, 2014 ... The proof of that is provided by the results of. FOUN. ORGANIZATIONS CAN EXPECT A RETURN. PURCHASE PRICE OF THE SIMULATO.

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assume (for simplicity) that vs the proof of that is provided