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The phrase "without any source" is grammatically correct and can be used in written English.
It is often used to describe something that is lacking a valid or credible origin or support. It can also be used to indicate that something is not backed up by evidence or proof. Example: The news article was filled with false information, without any source to back up its claims.
Exact(16)
■ Emotional exhaustion — emotionally overextended, drained and used up without any source of replenishment.
When buyers stop doing business in the area, the miners may find themselves without any source of income.
Instead, it has seen the village as an adversary and embarked on convoluted initiatives like a "housing fund" without any source of financing and an "inclusionary" zoning law, which would impose the burden of creating affordable housing on developers rather than providing incentives.
Current and former ministers have claimed that thousands of women have been imported into the UK and forced to work as sex slaves, but most of these statements were either based on distortions of quoted sources or fabrications without any source at all.
"It is not reasonable to expect people to live without any source of income for two weeks," said Dame Anne.
However, even in such complex scenarios, Directional BSS can produce an acceptable estimate of the RTF without any source activity detection.
Similar(44)
Without any sources of heat, the densest gas near the center of the map should cool to much lower temperatures as energy is lost because of radiation.
The results of this studies were obtained without any sources of funding.
Again, Outfoxed watchers will note the use of "some reports" as another version on "some people say", Fox's way of inserting their slant into news broadcasts without any sourcing.
This cross-sectional epidemiological study collected health data for 2,470 school children between 5 and 14 years of age (89% of eligible children) who had lived most of their lives in either one of two counties strongly impacted by industrial pollution (Bitterfeld and Hettstedt) or in a neighboring county without any sources of industrial pollution (Zerbst).
Self plagiarism is also considered ethically unacceptable: it occurs when one uses he's own previously published work (or parts of it) without citing any source.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com